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## The approximation of the pressure by a mixed method in the simulation of miscible displacement

RAIRO. Anal. numér., 17 1 (1983) 17-33

## Formulations and Numerical Methods of the Black Oil Model in Porous Media

Zhangxin Chen
SIAM Journal on Numerical Analysis 38 (2) 489 (2000)
DOI: 10.1137/S0036142999304263

## A Second Order Characteristic Method for Approximating Incompressible Miscible Displacement in Porous Media

Tongjun Sun and Keying Ma
International Journal of Mathematics and Mathematical Sciences 2012 1 (2012)
DOI: 10.1155/2012/870402

## Convergence analysis of an upwind mixed element method for advection diffusion problems

Zhitao Li
Applied Mathematics and Computation 212 (2) 318 (2009)
DOI: 10.1016/j.amc.2009.02.018

## On a Miscible Displacement Model in Porous Media Flow with Measure Data

Jérôme Droniou and Kyle S. Talbot
SIAM Journal on Mathematical Analysis 46 (5) 3158 (2014)
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J.E. Roberts and J.-M. Thomas
2 523 (1991)
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## An approximation of incompressible miscible displacement in porous media by mixed finite element method and characteristics-mixed finite element method

Tongjun Sun and Yirang Yuan
Journal of Computational and Applied Mathematics 228 (1) 391 (2009)
DOI: 10.1016/j.cam.2008.09.029

## A Numerical Approximation Structured by Mixed Finite Element and Upwind Fractional Step Difference for Semiconductor Device with Heat Conduction and Its Numerical Analysis

Yirang Yuan, Qing Yang, Changfeng Li and Tongjun Sun
Numerical Mathematics: Theory, Methods and Applications 10 (3) 541 (2017)
DOI: 10.4208/nmtma.2017.y15013

## Fully Discrete Finite Element Analysis of Multiphase Flow in Groundwater Hydrology

Zhangxin Chen and Richard E. Ewing
SIAM Journal on Numerical Analysis 34 (6) 2228 (1997)
DOI: 10.1137/S0036142995290063

## A posteriori error estimates, stopping criteria, and adaptivity for two-phase flows

Martin Vohralík and Mary F. Wheeler
Computational Geosciences 17 (5) 789 (2013)
DOI: 10.1007/s10596-013-9356-0

## Locally Conservative Coupling of Stokes and Darcy Flows

Béatrice Rivière and Ivan Yotov
SIAM Journal on Numerical Analysis 42 (5) 1959 (2005)
DOI: 10.1137/S0036142903427640

## Asymptotic production behavior in waterflooded oil reservoirs: Decline curves on a simplified model

A. Abbaszadeh, D. Bresch, B. Desjardins and E. Grenier
European Journal of Mechanics - B/Fluids 43 131 (2014)
DOI: 10.1016/j.euromechflu.2013.08.002

## Multistep characteristic method for incompressible flow in porous media

Xiaohan Long and Yirang Yuan
Applied Mathematics and Computation 214 (1) 259 (2009)
DOI: 10.1016/j.amc.2009.03.085

## A semi-discrete central scheme for scalar hyperbolic conservation laws with heterogeneous storage coefficient and its application to porous media flow

M.R. Correa and M.R. Borges
International Journal for Numerical Methods in Fluids 73 (3) 205 (2013)
DOI: 10.1002/fld.3794

## A priori error estimates of multiblock mortar expanded mixed method for elliptic problems

Applied Numerical Mathematics 157 670 (2020)
DOI: 10.1016/j.apnum.2020.03.011

## Two-grid mixed finite-element methods for nonlinear Schrödinger equations

Li Wu
Numerical Methods for Partial Differential Equations 28 (1) 63 (2012)
DOI: 10.1002/num.20607

## High-order bound-preserving finite difference methods for miscible displacements in porous media

Hui Guo, Xinyuan Liu and Yang Yang
Journal of Computational Physics 406 109219 (2020)
DOI: 10.1016/j.jcp.2019.109219

## Numerical study of theHP version of mixed discontinuous finite element methods for reaction-diffusion problems: The 1D case

Hongsen Chen, Zhangxin Chen and Baoyan Li
Numerical Methods for Partial Differential Equations 19 (4) 525 (2003)
DOI: 10.1002/num.10063

## Superconvergence of the Velocity Along the Gauss Lines in Mixed Finite Element Methods

R. E. Ewing, R. D. Lazarov and J. Wang
SIAM Journal on Numerical Analysis 28 (4) 1015 (1991)
DOI: 10.1137/0728054
Richard E. Ewing
233 (1994)
DOI: 10.1007/978-94-011-0896-6_19

## Two-grid methods for mixed finite-element solution of coupled reaction-diffusion systems

Li Wu and Myron B. Allen
Numerical Methods for Partial Differential Equations 15 (5) 589 (1999)
DOI: 10.1002/(SICI)1098-2426(199909)15:5<589::AID-NUM6>3.0.CO;2-W

## DOMAIN DECOMPOSITION ALGORITHM FOR TWO PHASE DISPLACEMENT PROBLEM IN POROUS MEDIA

Hongxing Rui
Acta Mathematica Scientia 18 5 (1998)
DOI: 10.1016/S0252-9602(17)30870-6

## Error Estimates of H1-Galerkin Mixed Finite Element Methods for Nonlinear Parabolic Problem

Hai Tao Che
Advanced Materials Research 267 504 (2011)
DOI: 10.4028/www.scientific.net/AMR.267.504

## Velocity weighting techniques for fluid displacement problems

R.E. Ewing, R.F. Heinemann, J.V. Koebbe and U.S. Prasad
Computer Methods in Applied Mechanics and Engineering 64 (1-3) 137 (1987)
DOI: 10.1016/0045-7825(87)90037-5

## A multiscale algorithm for the mineralization process during supercritical carbon dioxide injection into a deep saline aquifer

Luiz Umberto Rodrigues Sica
International Journal of Numerical Methods for Heat & Fluid Flow 30 (6) 3101 (2019)
DOI: 10.1108/HFF-09-2018-0494

## An optimal-order error estimate of the lowest-order ELLAM-MFEM approximation to miscible displacement in three space dimensions

Hong Wang and Xiangcheng Zheng
Journal of Computational and Applied Mathematics 375 112819 (2020)
DOI: 10.1016/j.cam.2020.112819

## Numerical analysis of a mixed finite element method for a flow-transport problem

S.-H. Chou and Q. Li
Numerical Methods for Partial Differential Equations 12 (2) 221 (1996)
DOI: 10.1002/(SICI)1098-2426(199603)12:2<221::AID-NUM5>3.0.CO;2-S

## Regularity of the Diffusion-Dispersion Tensor and Error Analysis of Galerkin FEMs for a Porous Medium Flow

SIAM Journal on Numerical Analysis 53 (3) 1418 (2015)
DOI: 10.1137/140958803

## ON THE APPROXIMATION OF INCOMPRESSIBLE MISCIBLE DISPLACEMENT PROBLEMS IN POROUS MEDIA BY MIXED AND STANDARD FINITE VOLUME ELEMENT METHODS

SARVESH KUMAR
International Journal of Modeling, Simulation, and Scientific Computing 04 (03) 1350013 (2013)
DOI: 10.1142/S179396231350013X

## A posteriori error estimates of mixed methods for miscible displacement problems

Yanping Chen and Wenbin Liu
International Journal for Numerical Methods in Engineering 73 (3) 331 (2008)
DOI: 10.1002/nme.2075

## An Optimal-Order Error Estimate for a Family of ELLAM-MFEM Approximations to Porous Medium Flow

Hong Wang
SIAM Journal on Numerical Analysis 46 (4) 2133 (2008)
DOI: 10.1137/S0036142903428281

## Maximum-principle-preserving third-order local discontinuous Galerkin method for convection-diffusion equations on overlapping meshes

Jie Du and Yang Yang
Journal of Computational Physics 377 117 (2019)
DOI: 10.1016/j.jcp.2018.10.034

## Computational engineering and science methodologies for modeling and simulation of subsurface applications

Mary F. Wheeler and Małgorzata Peszyńska
Advances in Water Resources 25 (8-12) 1147 (2002)
DOI: 10.1016/S0309-1708(02)00105-7

## Error Estimates for a Finite Element Method for the Drift Diffusion Semiconductor Device Equations

Zhangxin Chen and Bernardo Cockburn
SIAM Journal on Numerical Analysis 31 (4) 1062 (1994)
DOI: 10.1137/0731056

## A Block Finite Difference Scheme for Second-Order Elliptic Problems with Discontinuous Coefficients

Jian Shen
SIAM Journal on Numerical Analysis 33 (2) 686 (1996)
DOI: 10.1137/0733035

## On superconvergence techniques

Michal Křížek and Pekka Neittaanmäki
Acta Applicandae Mathematicae 9 (3) 175 (1987)
DOI: 10.1007/BF00047538

## Higher-order gradient post-processings for second-order elliptic problems

Abimael F.D. Loula, Fernando A. Rochinha and Márcio A. Murad
Computer Methods in Applied Mechanics and Engineering 128 (3-4) 361 (1995)
DOI: 10.1016/0045-7825(95)00885-3

## Mixed finite element methods for computing groundwater velocities

M. B. Allen, R. E. Ewing and J. V. Koebbe
Numerical Methods for Partial Differential Equations 1 (3) 195 (1985)
DOI: 10.1002/num.1690010304
James Glimm, Brent Lindquist and Qiang Zhang
29 123 (1991)
DOI: 10.1007/978-1-4613-9121-0_10

## A two‐grid method for characteristic expanded mixed finite element solution of miscible displacement problem

Hanzhang Hu and Yanping Chen
Numerical Linear Algebra with Applications 27 (3) (2020)
DOI: 10.1002/nla.2292

## Numerical analysis of a stabilized finite element method for tracer injection simulations

Sandra M.C. Malta, Abimael F.D. Loula and Eduardo L.M. Garcia
Computer Methods in Applied Mechanics and Engineering 187 (1-2) 119 (2000)
DOI: 10.1016/S0045-7825(99)00113-9
Myron B. Allen and Zhonghe Wang
12 1375 (1994)
DOI: 10.1007/978-94-010-9204-3_166

## Multiscale Simulations for Coupled Flow and Transport Using the Generalized Multiscale Finite Element Method

Eric Chung, Yalchin Efendiev, Wing Leung and Jun Ren
Computation 3 (4) 670 (2015)
DOI: 10.3390/computation3040670

## Finite difference method and its convergent error analyses for thermistor problem

Weidong Zhao
Applied Mathematics-A Journal of Chinese Universities 14 (3) 349 (1999)
DOI: 10.1007/s11766-999-0045-7

## An a posteriori-based, fully adaptive algorithm with adaptive stopping criteria and mesh refinement for thermal multiphase compositional flows in porous media

Daniele A. Di Pietro, Martin Vohralík and Soleiman Yousef
Computers & Mathematics with Applications 68 (12) 2331 (2014)
DOI: 10.1016/j.camwa.2014.08.008

## Two‐grid method for miscible displacement problem with dispersion by finite element method of characteristics

Yanping Chen and Hanzhang Hu
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 101 (3) (2021)
DOI: 10.1002/zamm.201900275

## Analysis of two-grid methods for reaction-diffusion equations by expanded mixed finite element methods

Yanping Chen, Huan-Wen Liu and Shang Liu
International Journal for Numerical Methods in Engineering 69 (2) 408 (2007)
DOI: 10.1002/nme.1775
Chen Y. Chiang, Clint N. Dawson and Mary F. Wheeler
667 (1991)
DOI: 10.1007/978-94-017-2199-8_12

## A time-stepping procedure based on convolution for the mixed finite element approximation for porous media flow

Aijie Cheng, Yongqiang Ren and Kaihua Xi
Applied Mathematics and Computation 218 (9) 5319 (2012)
DOI: 10.1016/j.amc.2011.11.015

## Finite element simulations for compressible miscible displacement with molecular dispersion in porous media

Huanzhen Chen and Qian Li
Applied Mathematics 11 (1) 17 (1996)
DOI: 10.1007/BF02662177
Hameeda Oda Al-Humedi and Ali Kamil Al-Abadi
2235 020010 (2020)
DOI: 10.1063/5.0007637

## The method of mixed volume element-characteristic mixed volume element and its numerical analysis for three-dimensional slightly compressible two-phase displacement

Yirang Yuan, Tongjun Sun, Changfeng Li and Qing Yang
Numerical Methods for Partial Differential Equations 34 (2) 661 (2018)
DOI: 10.1002/num.22220

## Mixed finite element approximation of phase velocities in compositional reservoir simulation

R.E. Ewing and R.F. Heinemann
Computer Methods in Applied Mechanics and Engineering 47 (1-2) 161 (1984)
DOI: 10.1016/0045-7825(84)90052-5

## A Mixed Method for the Mixed Initial-Boundary Value Problems of Equations of Semiconductor Devices

Jiang Zhu, Hongwei Wu and Yuanming Wang
SIAM Journal on Numerical Analysis 31 (3) 731 (1994)
DOI: 10.1137/0731039

## Adaptive Mesh Refinement and Multilevel Iteration for Flow in Porous Media

Richard D. Hornung and John A. Trangenstein
Journal of Computational Physics 136 (2) 522 (1997)
DOI: 10.1006/jcph.1997.5779

## Characteristics—Galerkin and mixed finite element approximation of contamination by compressible nuclear waste-disposal in porous media

So-Hsiang Chou and Qian Li
Numerical Methods for Partial Differential Equations 12 (3) 315 (1996)
DOI: 10.1002/(SICI)1098-2426(199605)12:3<315::AID-NUM3>3.0.CO;2-R

## Domain decomposition procedures combined withH1-Galerkin mixed finite element method for parabolic equation

Tongjun Sun and Keying Ma
Journal of Computational and Applied Mathematics 267 33 (2014)
DOI: 10.1016/j.cam.2014.01.036

## Modeling full-tensor anisotropy in groundwater flow via an iterative scheme for mixed finite elements

Zhonghe Wang and Myron B. Allen
Transport in Porous Media 25 (2) 147 (1996)
DOI: 10.1007/BF00135853

## A posteriori error estimates, stopping criteria, and adaptivity for multiphase compositional Darcy flows in porous media

Daniele A. Di Pietro, Eric Flauraud, Martin Vohralík and Soleiman Yousef
Journal of Computational Physics 276 163 (2014)
DOI: 10.1016/j.jcp.2014.06.061
J. Chapman and M. Jensen
323 (2013)
DOI: 10.1007/978-3-642-33134-3_35

## A posteriori error of a discontinuous Galerkin scheme for compressible miscible displacement problems with molecular diffusion and dispersion

Jiming Yang
International Journal for Numerical Methods in Fluids 65 (7) 781 (2011)
DOI: 10.1002/fld.2208
Helge K. Dahle, Magne S. Espedal and Richard E. Ewing
11 77 (1988)
DOI: 10.1007/978-1-4684-6352-1_5
Fengxin Chen and Huanzhen Chen
144 233 (2012)
DOI: 10.1007/978-3-642-27326-1_30

## Optimal error estimates and recovery technique of a mixed finite element method for nonlinear thermistor equations

Huadong Gao, Weiwei Sun and Chengda Wu
IMA Journal of Numerical Analysis 41 (4) 3175 (2021)
DOI: 10.1093/imanum/draa063

## An ELLAM-MFEM Solution Technique for Compressible Fluid Flows in Porous Media with Point Sources and Sinks

Hong Wang, Dong Liang, Richard E. Ewing, Stephen L. Lyons and Guan Qin
Journal of Computational Physics 159 (2) 344 (2000)
DOI: 10.1006/jcph.2000.6450

## A combined mixed finite element method and local discontinuous Galerkin method for miscible displacement problem in porous media

Hui Guo, QingHua Zhang and Yang Yang
Science China Mathematics 57 (11) 2301 (2014)
DOI: 10.1007/s11425-014-4879-y

## A splitting positive definite mixed element method for miscible displacement of compressible flow in porous media

Danping Yang
Numerical Methods for Partial Differential Equations 17 (3) 229 (2001)
DOI: 10.1002/num.3

## Convergence of an upwind control-volume mixed finite element method for convection–diffusion problems

H. Rui
Computing 81 (4) 297 (2007)
DOI: 10.1007/s00607-007-0256-9

## Efficient adaptive procedures for fluid-flow applications

Richard E. Ewing
Computer Methods in Applied Mechanics and Engineering 55 (1-2) 89 (1986)
DOI: 10.1016/0045-7825(86)90087-3

## Two-Grid Method for Nonlinear Reaction-Diffusion Equations by Mixed Finite Element Methods

Luoping Chen and Yanping Chen
Journal of Scientific Computing 49 (3) 383 (2011)
DOI: 10.1007/s10915-011-9469-3

## Characteristic petrov-galerkin subdomain methods for two-phase immiscible flow

Magne S. Espedal and Richard E. Ewing
Computer Methods in Applied Mechanics and Engineering 64 (1-3) 113 (1987)
DOI: 10.1016/0045-7825(87)90036-3

## A mixed-finite volume element coupled with the method of characteristic fractional step difference for simulating transient behavior of semiconductor device of heat conductor and its numerical analysis

Yi-rang Yuan, Qing Yang, Chang-feng Li and Tong-jun Sun
Acta Mathematicae Applicatae Sinica, English Series 33 (4) 1053 (2017)
DOI: 10.1007/s10255-017-0721-y

## Mixed finite volume element-upwind mixed volume element of compressible two-phase displacement and its numerical analysis

Yirang Yuan, Changfeng Li and Huailing Song
Journal of Computational and Applied Mathematics 370 112637 (2020)
DOI: 10.1016/j.cam.2019.112637

## Improved error estimates for mixed finite-element approximations for nonlinear parabolic equations: The continuous-time case

Sonia M. F. Garcia
Numerical Methods for Partial Differential Equations 10 (2) 129 (1994)
DOI: 10.1002/num.1690100202

## TWO-SCALE PRODUCT APPROXIMATION FOR SEMILINEAR PARABOLIC PROBLEMS IN MIXED METHODS

Dongho Kim, Eun-Jae Park and Boyoon Seo
Journal of the Korean Mathematical Society 51 (2) 267 (2014)
DOI: 10.4134/JKMS.2014.51.2.267

## Mixed methods for compressible miscible displacement with the effect of molecular dispersion

Qian Li and So-Hsiang Chou
Acta Mathematicae Applicatae Sinica 11 (2) 123 (1995)
DOI: 10.1007/BF02013148
R.E. EWING
5 251 (1986)
DOI: 10.1016/B978-0-444-42697-0.50037-0

## The expanded upwind-mixed method on changing meshes for positive semi-definite problem of two-phase miscible flow

Huailing Song, Yirang Yuan and Gongjie Liu
International Journal of Computer Mathematics 85 (7) 1113 (2008)
DOI: 10.1080/00207160701478680

## Superconvergence in the Pressure in the Simulation of Miscible Displacement

Jim Douglas, Jr.
SIAM Journal on Numerical Analysis 22 (5) 962 (1985)
DOI: 10.1137/0722058

## A new discontinuous Galerkin mixed finite element method for compressible miscible displacement problem

Jiansong Zhang and Huiran Han
Computers & Mathematics with Applications 80 (6) 1714 (2020)
DOI: 10.1016/j.camwa.2020.08.008

## Mixed volume element with characteristic mixed volume element method for compressible contamination treatment from nuclear waste

Yirang Yuan, Changfeng Li, Tongjun Sun and Qing Yang
International Journal of Computer Mathematics 98 (1) 136 (2021)
DOI: 10.1080/00207160.2020.1734795

## Well-Conditioned Iterative Schemes for Mixed Finite-Element Models of Porous-Media Flows

Myron B. Allen, Richard E. Ewing and Peng Lu
SIAM Journal on Scientific and Statistical Computing 13 (3) 794 (1992)
DOI: 10.1137/0913047

## Convergence analysis of mixed volume element-characteristic mixed volume element for three-dimensional chemical oil-recovery seepage coupled problem

Yirang YUAN, Aijie CHENG, Dangping YANG, Changfeng LI and Qing YANG
Acta Mathematica Scientia 38 (2) 519 (2018)
DOI: 10.1016/S0252-9602(18)30764-1

## A low order characteristic-nonconforming finite element method for nonlinear Sobolev equation with convection-dominated term

Dongyang Shi, Qili Tang and Wei Gong
Mathematics and Computers in Simulation 114 25 (2015)
DOI: 10.1016/j.matcom.2014.03.008

## Characteristic mixed volume element for compressible two-phase displacement in porous media

Changfeng Li, Yirang Yuan and Qing Yang
International Journal of Computer Mathematics 98 (11) 2233 (2021)
DOI: 10.1080/00207160.2021.1884233

## Analysis of fully discrete FEM for miscible displacement in porous media with Bear–Scheidegger diffusion tensor

Wentao Cai, Buyang Li, Yanping Lin and Weiwei Sun
Numerische Mathematik 141 (4) 1009 (2019)
DOI: 10.1007/s00211-019-01030-0

## Some Improved Error Estimates for the Modified Method of Characteristics

C. N. Dawson, T. F. Russell and M. F. Wheeler
SIAM Journal on Numerical Analysis 26 (6) 1487 (1989)
DOI: 10.1137/0726087

## Error analysis in $L^p \leqslant p \leqslant \infty$, for mixed finite element methods for linear and quasi-linear elliptic problems

Ricardo G. Durán
ESAIM: Mathematical Modelling and Numerical Analysis 22 (3) 371 (1988)
DOI: 10.1051/m2an/1988220303711

## A time-discretization procedure for a mixed finite element approximation of miscible displacement in porous media

Jim Jr. Douglas, Richard E. Ewing and Mary Fanett Wheeler
RAIRO. Analyse numérique 17 (3) 249 (1983)
DOI: 10.1051/m2an/1983170302491

## Compositional Modeling by the Combined Discontinuous Galerkin and Mixed Methods

SPE Journal 11 (01) 19 (2006)
DOI: 10.2118/90276-PA

## A Broken P1-Nonconforming Finite Element Method for Incompressible Miscible Displacement Problem in Porous Media

Fengxin Chen and Huanzhen Chen
ISRN Applied Mathematics 2013 1 (2013)
DOI: 10.1155/2013/498383
Todd Arbogast, Jim Douglas and Juan E. Santos
11 47 (1988)
DOI: 10.1007/978-1-4684-6352-1_3

## An efficient two grid method for miscible displacement problem approximated by mixed finite element methods

Shang Liu, Yanping Chen, Yunqing Huang and Jie Zhou
Computers & Mathematics with Applications 77 (3) 752 (2019)
DOI: 10.1016/j.camwa.2018.10.013

## Superconvergence of a combined mixed finite element and discontinuous Galerkin approximation for an incompressible miscible displacement problem

Jiming Yang and Yanping Chen
Applied Mathematical Modelling 36 (3) 1106 (2012)
DOI: 10.1016/j.apm.2011.07.054

## Two-grid method for compressible miscible displacement problem by mixed finite element methods and expanded mixed finite element method of characteristics

Hanzhang Hu
Numerical Algorithms 89 (2) 611 (2022)
DOI: 10.1007/s11075-021-01127-4

## Unified Convergence Analysis of Numerical Schemes for a Miscible Displacement Problem

Jérôme Droniou, Robert Eymard, Alain Prignet and Kyle S. Talbot
Foundations of Computational Mathematics 19 (2) 333 (2019)
DOI: 10.1007/s10208-018-9387-y

## Mixed finite elements and Newton-type linearizations for the solution of Richards' equation

Luca Bergamaschi and Mario Putti
International Journal for Numerical Methods in Engineering 45 (8) 1025 (1999)
DOI: 10.1002/(SICI)1097-0207(19990720)45:8<1025::AID-NME615>3.0.CO;2-G

## A Fully Conservative Eulerian-Lagrangian Stream-Tube Method for Advection-Diffusion Problems

Todd Arbogast, Chieh-Sen Huang and Chen-Hui Hung
SIAM Journal on Scientific Computing 34 (4) B447 (2012)
DOI: 10.1137/110840376

## Mixed Volume Element-Characteristic Fractional Step Difference Method for Contamination from Nuclear Waste Disposal

Changfeng Li, Yirang Yuan, Tongjun Sun and Qing Yang
Journal of Scientific Computing 72 (2) 467 (2017)
DOI: 10.1007/s10915-017-0365-3

## Superconvergence of mixed covolume method for elliptic problems on triangular grids

Chunjia Bi
Journal of Computational and Applied Mathematics 216 (2) 534 (2008)
DOI: 10.1016/j.cam.2007.06.002

## Fourier Analysis of Local Discontinuous Galerkin Methods for Linear Parabolic Equations on Overlapping Meshes

Nattaporn Chuenjarern and Yang Yang
Journal of Scientific Computing 81 (2) 671 (2019)
DOI: 10.1007/s10915-019-01030-0

## Numerical analysis of a nonlocal parabolic problem resulting from thermistor problem

Moulay Rchid Sidi Ammi and Delfim F.M. Torres
Mathematics and Computers in Simulation 77 (2-3) 291 (2008)
DOI: 10.1016/j.matcom.2007.08.013

## Finite element approximations of two-phase miscible incompressible displacement with discontinuous coefficients

Sun Wentao and Liu Yunxian
Applied Mathematics-A Journal of Chinese Universities 14 (4) 451 (1999)
DOI: 10.1007/s11766-999-0075-1

## Conservative numerical methods for the reinterpreted discrete fracture model on non-conforming meshes and their applications in contaminant transportation in fractured porous media

Hui Guo, Wenjing Feng, Ziyao Xu and Yang Yang
Advances in Water Resources 153 103951 (2021)

## Two-Grid method for nonlinear parabolic equations by expanded mixed finite element methods

Yanping Chen, Luoping Chen and Xiaochun Zhang
Numerical Methods for Partial Differential Equations 29 (4) 1238 (2013)
DOI: 10.1002/num.21753

## High-order bound-preserving discontinuous Galerkin methods for compressible miscible displacements in porous media on triangular meshes

Nattaporn Chuenjarern, Ziyao Xu and Yang Yang
Journal of Computational Physics 378 110 (2019)
DOI: 10.1016/j.jcp.2018.11.003

## A mixed element method for Darcy–Forchheimer incompressible miscible displacement problem

Hao Pan and Hongxing Rui
Computer Methods in Applied Mechanics and Engineering 264 1 (2013)
DOI: 10.1016/j.cma.2013.05.011

## An Optimal Error Estimates ofH1-Galerkin Expanded Mixed Finite Element Methods for Nonlinear Viscoelasticity-Type Equation

Haitao Che, Yiju Wang and Zhaojie Zhou
Mathematical Problems in Engineering 2011 1 (2011)
DOI: 10.1155/2011/570980

## Mixed covolume method for parabolic problems on triangular grids

Suxiang Yang and Ziwen Jiang
Applied Mathematics and Computation 215 (3) 1251 (2009)
DOI: 10.1016/j.amc.2009.06.068

## A MCC finite element approximation of incompressible miscible displacement in porous media

Xindong Li and Hongxing Rui
Computers & Mathematics with Applications 70 (5) 750 (2015)
DOI: 10.1016/j.camwa.2015.05.018

## Parallel algorithm combined with mixed element procedure for compressible miscible displacement problem

Jiansong Zhang, Danping Yang, Hui Guo and Yan Qu
Numerical Algorithms 76 (4) 993 (2017)
DOI: 10.1007/s11075-017-0294-0

## A priori estimates for mixed finite element methods for the wave equation

Lawrence C. Cowsat, Todd F. Dupont and Mary F. Wheeler
Computer Methods in Applied Mechanics and Engineering 82 (1-3) 205 (1990)
DOI: 10.1016/0045-7825(90)90165-I

## AnH1-Galerkin Mixed Finite Element Method for Parabolic Partial Differential Equations

Amiya K. Pani
SIAM Journal on Numerical Analysis 35 (2) 712 (1998)
DOI: 10.1137/S0036142995280808

## New analysis of Galerkin-mixed FEMs for incompressible miscible flow in porous media

Weiwei Sun and Chengda Wu
Mathematics of Computation 90 (327) 81 (2020)
DOI: 10.1090/mcom/3561

## Numerical methods for a model for compressible miscible displacement in porous media

Jim Douglas and Jean E. Roberts
Mathematics of Computation 41 (164) 441 (1983)
DOI: 10.1090/S0025-5718-1983-0717695-3

## Convergence Analysis of a Mixed Finite Volume Scheme for an Elliptic-Parabolic System Modeling Miscible Fluid Flows in Porous Media

Claire Chainais-Hillairet and Jérôme Droniou
SIAM Journal on Numerical Analysis 45 (5) 2228 (2007)
DOI: 10.1137/060657236

## A Finite Volume Scheme for Two-Phase Immiscible Flow in Porous Media

Anthony Michel
SIAM Journal on Numerical Analysis 41 (4) 1301 (2003)
DOI: 10.1137/S0036142900382739

## Parallel Nonoverlapping DDM Combined with the Characteristic Method for Incompressible Miscible Displacements in Porous Media

Keying Ma and Tongjun Sun
Advances in Numerical Analysis 2013 1 (2013)
DOI: 10.1155/2013/303952

## A MIXED FINITE ELEMENT APPROXIMATION FOR COMPRESSIBLE FLOW OF CONTAMINATION FROM NUCLEAR WASTE IN POROUS MEDIA

S.H. Chou and Qian Li
Acta Mathematica Scientia 18 (2) 146 (1998)
DOI: 10.1016/S0252-9602(17)30747-6

## A computationally efficient modification of mixed finite element methods for flow problems with full transmissivity tensors

Joe Koebbe
Numerical Methods for Partial Differential Equations 9 (4) 339 (1993)
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## A two-grid method for mixed finite-element solution of reaction-diffusion equations

Li Wu and Myron B. Allen
Numerical Methods for Partial Differential Equations 15 (3) 317 (1999)
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## Two-grid methods for semilinear time fractional reaction diffusion equations by expanded mixed finite element method

Qingfeng Li, Yanping Chen, Yunqing Huang and Yang Wang
Applied Numerical Mathematics 157 38 (2020)
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## Superconvergence for a time-discretization procedure for the mixed finite element approximation of miscible displacement in porous media

Aijie Cheng, Kaixin Wang and Hong Wang
Numerical Methods for Partial Differential Equations 28 (4) 1382 (2012)
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## A combined hybrid mixed element method for incompressible miscible displacement problem with local discontinuous Galerkin procedure

Jiansong Zhang, Huiran Han, Hui Guo and Xiaomang Shen
Numerical Methods for Partial Differential Equations 36 (6) 1629 (2020)
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## A new MCC–MFE method for compressible miscible displacement in porous media

Xindong Li, Hongxing Rui and Wenwen Xu
Journal of Computational and Applied Mathematics 302 139 (2016)
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## A novel approach for subsurface characterization of coupled fluid flow and geomechanical deformation: the case of slightly compressible flows

M. R. Borges and F. Pereira
Computational Geosciences 24 (4) 1693 (2020)
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## Expanded mixed finite element methods for linear second-order elliptic problems, I

Zhangxin Chen
ESAIM: Mathematical Modelling and Numerical Analysis 32 (4) 479 (1998)
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## A Multipoint Flux Mixed Finite Element Method for Darcy–Forchheimer Incompressible Miscible Displacement Problem

Wenwen Xu, Dong Liang, Hongxing Rui and Xindong Li
Journal of Scientific Computing 82 (1) (2020)
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## Block iterative solvers for higher order finite volume methods

Do Y. Kwak and Hijin Lee
Journal of Computational and Applied Mathematics 232 (2) 378 (2009)
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## Superconvergence and Postprocessing of Fluxes from Lowest-Order Mixed Methods on Triangles and Tetrahedra

Todd F. Dupont and Philip T. Keenan
SIAM Journal on Scientific Computing 19 (4) 1322 (1998)
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## On the Stability of Pressure and Velocity Computations for Heterogeneous Reservoirs

Are Magnus Bruaset and Bjørn Fredrik Nielsen
SIAM Journal on Applied Mathematics 56 (4) 994 (1996)
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## Simulation of miscible displacement in porous media by a modified Uzawa's algorithm combined with a characteristic method

Daoqi Yang
Computer Methods in Applied Mechanics and Engineering 162 (1-4) 359 (1998)
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## Error analysis of mixed finite element method for Poisson‐Nernst‐Planck system

Mingyan He and Pengtao Sun
Numerical Methods for Partial Differential Equations 33 (6) 1924 (2017)
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## Two-grid methods for miscible displacement problem by Galerkin methods and mixed finite-element methods

Shang Liu, Yanping Chen, Yunqing Huang and Jie Zhou
International Journal of Computer Mathematics 95 (8) 1453 (2018)
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## Superconvergence Analysis of a Full-Discrete Combined Mixed Finite Element and Discontinuous Galerkin Approximation for an Incompressible Miscible Displacement Problem

Jiming Yang and Zhiguang Xiong
Acta Applicandae Mathematicae 142 (1) 107 (2016)
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## A New Two-Grid Method for Expanded Mixed Finite Element Solution of Nonlinear Reaction Diffusion Equations

Shang Liu and Yanping Chen
Advances in Applied Mathematics and Mechanics 9 (3) 757 (2017)
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## Bound-Preserving Discontinuous Galerkin Method for Compressible Miscible Displacement in Porous Media

Hui Guo and Yang Yang
SIAM Journal on Scientific Computing 39 (5) A1969 (2017)
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## -Galerkin mixed finite element methods for pseudo-hyperbolic equations

Yang Liu and Hong Li
Applied Mathematics and Computation 212 (2) 446 (2009)
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## An optimal-order error estimate for a Galerkin-mixed finite-element time-stepping procedure for porous media flows

Feng-xin Chen, Huan-zhen Chen and Hong Wang
Numerical Methods for Partial Differential Equations 28 (2) 707 (2012)
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## Mixed finite element analysis for the Poisson–Nernst–Planck/Stokes coupling

Mingyan He and Pengtao Sun
Journal of Computational and Applied Mathematics 341 61 (2018)
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## An Iterative Perturbation Method for the Pressure Equation in the Simulation of Miscible Displacement in Porous Media

Ping Lin and Daoqi Yang
SIAM Journal on Scientific Computing 19 (3) 893 (1998)
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## Superconvergent error estimates for a class of discretization methods for a coupled first-order system with discontinuous coefficients

Richard E. Ewing and Jian Shen
Numerical Methods for Partial Differential Equations 15 (3) 267 (1999)
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## An upwind approximation combined with mixed volume element for a positive semi-definite contamination treatment from nuclear waste

Changfeng Li, Yirang Yuan and Huailing Song
Engineering with Computers 36 (4) 1599 (2020)
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## Mathematical theory of stationary miscible filtration

A Mikelić
Journal of Differential Equations 90 (1) 186 (1991)
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## Discontinuous Galerkin Finite Element Convergence for Incompressible Miscible Displacement Problems of Low Regularity

Sören Bartels, Max Jensen and Rüdiger Müller
SIAM Journal on Numerical Analysis 47 (5) 3720 (2009)
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## Analysis of Lowest-Order Characteristics-Mixed FEMs for Incompressible Miscible Flow in Porous Media

Weiwei Sun
SIAM Journal on Numerical Analysis 59 (4) 1875 (2021)
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## A new MMOCAA-MFE method for compressible miscible displacement in porous media

Jiansong Zhang, Danping Yang, Shuqian Shen and Jiang Zhu
Applied Numerical Mathematics 80 65 (2014)
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## Local Discontinuous Galerkin Method for Incompressible Miscible Displacement Problem in Porous Media

Hui Guo, Fan Yu and Yang Yang
Journal of Scientific Computing 71 (2) 615 (2017)
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## Block‐centered upwind multistep difference method and convergence analysis for numerical simulation of oil reservoir

Yirang Yuan, Huailing Song, Changfeng Li and Tongjun Sun
Mathematical Methods in the Applied Sciences 42 (9) 3289 (2019)
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## A high order hybridizable discontinuous Galerkin method for incompressible miscible displacement in heterogeneous media

Maurice S. Fabien, Matthew Knepley and Beatrice Riviere
Results in Applied Mathematics 8 100089 (2020)
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## Finite element methods for nonlinear flows in porous media

Richard E. Ewing
Computer Methods in Applied Mechanics and Engineering 51 (1-3) 421 (1985)
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## A new combined characteristic mixed finite element method for compressible miscible displacement problem

Jiansong Zhang
Numerical Algorithms 81 (3) 1157 (2019)
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## The method of mixed volume element-characteristic mixed volume element and its numerical analysis for groundwater pollution in binary medium

Yirang Yuan, Ming Cui, Changfeng Li and Tongjun Sun
Applied Mathematics and Computation 362 124536 (2019)
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## A sufficient condition for the convergence of the inexact Uzawa algorithm for saddle point problems

Mingrong Cui
Journal of Computational and Applied Mathematics 139 (2) 189 (2002)
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## A combined discontinuous Galerkin finite element method for miscible displacement problem

Jiansong Zhang, Jiang Zhu, Rongpei Zhang, Danping Yang and Abimael F.D. Loula
Journal of Computational and Applied Mathematics 309 44 (2017)
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## Splitting positive definite mixed element methods for pseudo-hyperbolic equations

Yang Liu, Hong Li, Jinfeng Wang and Siriguleng He
Numerical Methods for Partial Differential Equations 28 (2) 670 (2012)
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## error estimates of two-grid schemes of expanded mixed finite element methods

Yanping Chen and Li Li
Applied Mathematics and Computation 209 (2) 197 (2009)
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Jim Douglas, Felipe Pereira and Li-Ming Yeh
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## Finite element approximation to initial-boundary value problems of the semiconductor device equations with magnetic influence

Jiang Zhu
Mathematics of Computation 59 (199) 39 (1992)
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## Mixed methods using standard conforming finite elements

Jichun Li, Todd Arbogast and Yunqing Huang
Computer Methods in Applied Mechanics and Engineering 198 (5-8) 680 (2009)
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## Convergence of an MPFA finite volume scheme for a two‐phase porous media flow model with dynamic capillarity

X Cao, S F Nemadjieu and I S Pop
IMA Journal of Numerical Analysis (2018)
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## Stabilized finite element methods for miscible displacement in porous media

Yuting Wei
ESAIM: Mathematical Modelling and Numerical Analysis 28 (5) 611 (1994)
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## Mixed volume element combined with characteristic mixed finite volume element method for oil–water two phase displacement problem

Yirang Yuan, Tongjun Sun, Changfeng Li, Yunxin Liu and Qing Yang
Journal of Computational and Applied Mathematics 340 404 (2018)
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## Two-grid method for compressible miscible displacement problem by CFEM–MFEM

Jiaoyan Zeng, Yanping Chen and Hanzhang Hu
Journal of Computational and Applied Mathematics 337 175 (2018)
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## A reduced-order finite element method based on POD for the incompressible miscible displacement problem

Junpeng Song and Hongxing Rui
Computers & Mathematics with Applications 98 99 (2021)
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## Efficient Time-Stepping Methods for Miscible Displacement Problems in Porous Media

Richard E. Ewing and Thomas F. Russell
SIAM Journal on Numerical Analysis 19 (1) 1 (1982)
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## Mathematical Analysis for Reservoir Models

Zhangxin Chen and Richard Ewing
SIAM Journal on Mathematical Analysis 30 (2) 431 (1999)
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## Error estimates of H 1-Galerkin mixed finite element method for Schrödinger equation

Yang Liu, Hong Li and Jin-feng Wang
Applied Mathematics-A Journal of Chinese Universities 24 (1) 83 (2009)
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## Mixed finite volume methods on nonstaggered quadrilateral grids for elliptic problems

So-Hsiang Chou, Do Kwak and Kwang Kim
Mathematics of Computation 72 (242) 525 (2002)
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## Convergence analysis of a DDFV scheme for a system describing miscible fluid flows in porous media

Claire Chainais-Hillairet, Stella Krell and Alexandre Mouton
Numerical Methods for Partial Differential Equations 31 (3) 723 (2015)
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## Characteristic mixed discontinuous finite element methods for advection-dominated diffusion problems

Zhangxin Chen
Computer Methods in Applied Mechanics and Engineering 191 (23-24) 2509 (2002)
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## Numerical method of mixed finite volume-modified upwind fractional step difference for three-dimensional semiconductor device transient behavior problems

Yirang YUAN, Qing YANG, Changfeng LI and Tongjun SUN
Acta Mathematica Scientia 37 (1) 259 (2017)
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## A two-grid method for incompressible miscible displacement problems by mixed finite element and Eulerian–Lagrangian localized adjoint methods

Yang Wang and Yanping Chen
Journal of Mathematical Analysis and Applications 468 (1) 406 (2018)
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## Some observations on mixed methods for fully nonlinear parabolic problems in divergence form

M.-Y. Kim, F.A. Milner and E.-J. Park
Applied Mathematics Letters 9 (1) 75 (1996)
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## Full discretization of time dependent convection–diffusion–reaction equation coupled with the Darcy system

Nancy Chalhoub, Pascal Omnes, Toni Sayah and Rebecca El Zahlaniyeh
Calcolo 57 (1) (2020)
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## Mixed Finite Element Method for Miscible Displacement Problems in Porous Media

B. L. Darlow, R. E. Ewing and M. F. Wheeler
Society of Petroleum Engineers Journal 24 (04) 391 (1984)
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## A combined mixed and discontinuous Galerkin method for compressible miscible displacement problem in porous media

Mingrong Cui
Journal of Computational and Applied Mathematics 198 (1) 19 (2007)
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## Stability analysis and error estimates of local discontinuous Galerkin methods for convection–diffusion equations on overlapping meshes

Jie Du, Yang Yang and Eric Chung
BIT Numerical Mathematics 59 (4) 853 (2019)
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## Conservative Local Discontinuous Galerkin Method for Compressible Miscible Displacements in Porous Media

Fan Yu, Hui Guo, Nattaporn Chuenjarern and Yang Yang
Journal of Scientific Computing 73 (2-3) 1249 (2017)
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## An approximation of incompressible miscible displacement in porous media by mixed finite elements and symmetric finite volume element method of characteristics

Zhe Yin, Hongxing Rui and Qiang Xu
Numerical Methods for Partial Differential Equations 29 (3) 897 (2013)
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## Numerical analysis for systems with memory arising from semiconductor simulations

W. Allegretto, Y. Lin and A. Zhou
Applied Mathematics and Computation 105 (2-3) 101 (1999)
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## WO-GRID METHOD FOR BURGERS’ EQUATION BY A NEW MIXED FINITE ELEMENT SCHEME

Xiaohui Hu, Pengzhan Huang and Xinlong Feng
Mathematical Modelling and Analysis 19 (1) 1 (2014)
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## An upwind-mixed method on changing meshes for two-phase miscible flow in porous media

Huailing Song and Yirang Yuan
Applied Numerical Mathematics 58 (6) 815 (2008)
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## A new two-grid mixed finite element analysis of semi-linear reaction–diffusion equation

Jiansong Zhang, Huiran Han, Yun Yu and Jun Liu
Computers & Mathematics with Applications 92 172 (2021)
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## Analysis of hp discontinuous Galerkin methods for incompressible two-phase flow

Yekaterina Epshteyn and Beatrice Rivière
Journal of Computational and Applied Mathematics 225 (2) 487 (2009)
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## A stabilized mixed finite element method for coupled Stokes and Darcy flows with transport

Hongxing Rui and Jingyuan Zhang
Computer Methods in Applied Mechanics and Engineering 315 169 (2017)
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## A mixed volume element with upwind multistep mixed volume element and convergence analysis for numerical simulation of nuclear waste contaminant disposal

Changfeng Li, Yirang Yuan and Huailing Song
Journal of Computational and Applied Mathematics 356 164 (2019)
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## Mixed methods with dynamic finite-element spaces for miscible displacement in porous media

Daoqi Yang
Journal of Computational and Applied Mathematics 30 (3) 313 (1990)
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## A finite element model for the time-dependent Joule heating problem

Charles M. Elliott and Stig Larsson
Mathematics of Computation 64 (212) 1433 (1995)
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## A virtual element method for the miscible displacement of incompressible fluids in porous media

L. Beirão da Veiga, A. Pichler and G. Vacca
Computer Methods in Applied Mechanics and Engineering 375 113649 (2021)
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## H1-Galerkin expanded mixed finite element methods for nonlinear pseudo-parabolic integro-differential equations

Haitao Che, Zhaojie Zhou, Ziwen Jiang and Yiju Wang
Numerical Methods for Partial Differential Equations 29 (3) 799 (2013)
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## A priori error estimates for interior penalty discontinuous Galerkin method applied to nonlinear Sobolev equations

Tongjun Sun and Danping Yang
Applied Mathematics and Computation 200 (1) 147 (2008)
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## A characteristic mixed method with dynamic finite-element space for convection-dominated diffusion problems

Daoqi Yang
Journal of Computational and Applied Mathematics 43 (3) 343 (1992)
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## Convergence analysis of an approximation of miscible displacement in porous media by mixed finite elements and a modified method of characteristics

Richard E. Ewing, Thomas F. Russell and Mary Fanett Wheeler
Computer Methods in Applied Mechanics and Engineering 47 (1-2) 73 (1984)
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## A priori error estimates of a combined mixed finite element and local discontinuous Galerkin method for an incompressible miscible displacement problem

Jiming Yang, Yanping Chen and Yunqing Huang
Applied Mathematics and Computation 334 141 (2018)
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## Numerical simulation for a incompressible miscible displacement problem using a reduced-order finite element method based on POD technique

Junpeng Song and Hongxing Rui
Computational Geosciences 25 (6) 2093 (2021)
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## Application of superconvergence to problems in the simulation of miscible displacement

R.E.E wing, J. Shen and J. Wang
Computer Methods in Applied Mechanics and Engineering 89 (1-3) 73 (1991)
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## Sharp algebraic and total a posteriori error bounds for h and p finite elements via a multilevel approach. Recovering mass balance in any situation

Jan Papež, Ulrich Rüde, Martin Vohralík and Barbara Wohlmuth
Computer Methods in Applied Mechanics and Engineering 371 113243 (2020)
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## An HMM–ELLAM scheme on generic polygonal meshes for miscible incompressible flows in porous media

Hanz Martin Cheng and Jérôme Droniou
Journal of Petroleum Science and Engineering 172 707 (2019)
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## On the Approximation of Miscible Displacement in Porous Media by a Method of Characteristics Combined with a Mixed Method

Ricardo G. Durán
SIAM Journal on Numerical Analysis 25 (5) 989 (1988)
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## Three-phase immiscible displacement in heterogeneous petroleum reservoirs

E. Abreu, J. Douglas, F. Furtado, D. Marchesin and F. Pereira
Mathematics and Computers in Simulation 73 (1-4) 2 (2006)
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## A mixed and discontinuous Galerkin finite volume element method for incompressible miscible displacement problems in porous media

Sarvesh Kumar
Numerical Methods for Partial Differential Equations 28 (4) 1354 (2012)
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## Error estimates for a mixed finite element discretization of a two-phase porous media flow model with dynamic capillarity

Xiulei Cao and Koondanibha Mitra
Journal of Computational and Applied Mathematics 353 164 (2019)
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## Substructure preconditioners for elliptic saddle point problems

Torgeir Rusten and Ragnar Winther
Mathematics of Computation 60 (201) 23 (1993)
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## Convergence analysis of an approximation to miscible fluid flows in porous media by combining mixed finite element and finite volume methods

Brahim Amaziane and Mustapha El Ossmani
Numerical Methods for Partial Differential Equations 24 (3) 799 (2008)
DOI: 10.1002/num.20291

## Timestepping Along Characteristics for a Mixed Finite-Element Approximation for Compressible Flow of Contamination from Nuclear Waste in Porous Media

Richard E. Ewing, Yirang Yuan and Gang Li
SIAM Journal on Numerical Analysis 26 (6) 1513 (1989)
DOI: 10.1137/0726088

## Partitioned coupling of advection–diffusion–reaction systems and Brinkman flows

Pietro Lenarda, Marco Paggi and Ricardo Ruiz Baier
Journal of Computational Physics 344 281 (2017)
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## Modified Method of Characteristics Combined with Finite Volume Element Methods for Incompressible Miscible Displacement Problems in Porous Media

International Journal of Partial Differential Equations 2014 1 (2014)
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## $$L^p$$ L p Error Estimates of Two-Grid Method for Miscible Displacement Problem

Yanping Chen, Jiaoyan Zeng and Jie Zhou
Journal of Scientific Computing 69 (1) 28 (2016)
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