Mortar finite element discretization of a model coupling Darcy and Stokes equations
ESAIM: M2AN, 42 3 (2008) 375-410
Published online: 2008-04-03
Articles citing this article
The Citing articles tool gives a list of articles citing the current article.
The citing articles come from EDP Sciences database, as well as other publishers participating in CrossRef Cited-by Linking Program. You can set up your personal account to receive an email alert each time this article is cited by a new article (see the menu on the right-hand side of the abstract page).
Cited article:
This article has been cited by the following article(s):
A scalar/vector stabilized hybrid mixed method for Darcy–Stokes flows
Iury IgrejaJournal of Computational and Applied Mathematics 473 116879 (2026)
https://doi.org/10.1016/j.cam.2025.116879
A mortar method for the coupled Stokes-Darcy problem using the MAC scheme for Stokes and mixed finite elements for Darcy
Wietse M. Boon, Dennis Gläser, Rainer Helmig, Kilian Weishaupt and Ivan YotovComputational Geosciences 28 (3) 413 (2024)
https://doi.org/10.1007/s10596-023-10267-6
An extended nonconforming finite element method for the coupled Darcy–Stokes problem
Pei Cao and Jinru ChenJournal of Computational and Applied Mathematics 451 116092 (2024)
https://doi.org/10.1016/j.cam.2024.116092
A decoupled stabilized finite element method for nonstationary stochastic shale oil model based on superhydrophobic material modification
Jian Li, Xinyue Zhang and Ruixia LiComputers & Mathematics with Applications 172 94 (2024)
https://doi.org/10.1016/j.camwa.2024.07.033
Block Preconditioners for the Marker-and-Cell Discretization of the Stokes–Darcy Equations
Chen Greif and Yunhui HeSIAM Journal on Matrix Analysis and Applications 44 (4) 1540 (2023)
https://doi.org/10.1137/22M1518384
A stochastic collocation method based on sparse grids for a stochastic Stokes-Darcy model
Zhipeng Yang, Xuejian Li, Xiaoming He and Ju MingDiscrete & Continuous Dynamical Systems - S 15 (4) 893 (2022)
https://doi.org/10.3934/dcdss.2021104
Local and parallel efficient BDF2 and BDF3 rotational pressure-correction schemes for a coupled Stokes/Darcy system
Jian Li, Xue Wang, Md. Abdullah Al Mahbub, Haibiao Zheng and Zhangxin ChenJournal of Computational and Applied Mathematics 412 114326 (2022)
https://doi.org/10.1016/j.cam.2022.114326
An extended finite element method for coupled Darcy–Stokes problems
Pei Cao and Jinru ChenInternational Journal for Numerical Methods in Engineering 123 (19) 4586 (2022)
https://doi.org/10.1002/nme.7047
Nonconforming time discretization based on Robin transmission conditions for the Stokes–Darcy system
Thi-Thao-Phuong Hoang, Hemanta Kunwar and Hyesuk LeeApplied Mathematics and Computation 413 126602 (2022)
https://doi.org/10.1016/j.amc.2021.126602
A Global-in-time Domain Decomposition Method for the Coupled Nonlinear Stokes and Darcy Flows
Thi-Thao-Phuong Hoang and Hyesuk LeeJournal of Scientific Computing 87 (1) (2021)
https://doi.org/10.1007/s10915-021-01422-1
Robin-Robin domain decomposition methods for the dual-porosity-conduit system
Jiangyong Hou, Wenjing Yan, Dan Hu and Zhengkang HeAdvances in Computational Mathematics 47 (1) (2021)
https://doi.org/10.1007/s10444-020-09828-5
A second-order fractional time-stepping method for a coupled Stokes/Darcy system
Jian Li, Rui Li, Xin Zhao and Zhangxin ChenJournal of Computational and Applied Mathematics 390 113329 (2021)
https://doi.org/10.1016/j.cam.2020.113329
A Compressible Fluid Flow Model Coupling Channel and Porous Media Flows and Its Application to Fuel Cell Materials
Alex Jarauta, Valentin Zingan, Peter Minev and Marc SecanellTransport in Porous Media 134 (2) 351 (2020)
https://doi.org/10.1007/s11242-020-01449-2
The efficient rotational pressure-correction schemes for the coupling Stokes/Darcy problem
Jian Li, Min Yao, Md. Abdullah Al Mahbub and Haibiao ZhengComputers & Mathematics with Applications 79 (2) 337 (2020)
https://doi.org/10.1016/j.camwa.2019.06.033
Adaptive partitioned methods for the time-accurate approximation of the evolutionary Stokes–Darcy system
Yi Li, Yanren Hou, William Layton and Haiyun ZhaoComputer Methods in Applied Mechanics and Engineering 364 112923 (2020)
https://doi.org/10.1016/j.cma.2020.112923
Mortar Element Method for the Time Dependent Coupling of Stokes and Darcy Flows
Yanping Chen, Xin Zhao and Yunqing HuangJournal of Scientific Computing 80 (2) 1310 (2019)
https://doi.org/10.1007/s10915-019-00977-4
A divergence free weak virtual element method for the Stokes–Darcy problem on general meshes
Gang Wang, Feng Wang, Long Chen and Yinnian HeComputer Methods in Applied Mechanics and Engineering 344 998 (2019)
https://doi.org/10.1016/j.cma.2018.10.022
A Crank–Nicolson discontinuous finite volume element method for a coupled non-stationary Stokes–Darcy problem
Rui Li, Yali Gao, Wenjing Yan and Zhangxin ChenJournal of Computational and Applied Mathematics 353 86 (2019)
https://doi.org/10.1016/j.cam.2018.12.025
Discontinuous Finite Volume Element Method for a Coupled Non-stationary Stokes–Darcy Problem
Rui Li, Yali Gao, Jian Li and Zhangxin ChenJournal of Scientific Computing 74 (2) 693 (2018)
https://doi.org/10.1007/s10915-017-0454-3
Well-posed Stokes/Brinkman and Stokes/Darcy coupling revisited with new jump interface conditions
Philippe AngotESAIM: Mathematical Modelling and Numerical Analysis 52 (5) 1875 (2018)
https://doi.org/10.1051/m2an/2017060
A stabilized finite volume method for the evolutionary Stokes–Darcy system
Yi Li, Yanren Hou and Rui LiComputers & Mathematics with Applications 75 (2) 596 (2018)
https://doi.org/10.1016/j.camwa.2017.09.039
A stabilized hybrid mixed DGFEM naturally coupling Stokes–Darcy flows
Iury Igreja and Abimael F.D. LoulaComputer Methods in Applied Mechanics and Engineering 339 739 (2018)
https://doi.org/10.1016/j.cma.2018.05.026
A Strongly Conservative Hybrid DG/Mixed FEM for the Coupling of Stokes and Darcy Flow
Guosheng Fu and Christoph LehrenfeldJournal of Scientific Computing 77 (3) 1605 (2018)
https://doi.org/10.1007/s10915-018-0691-0
A posteriori error analysis of the fully discretized time-dependent coupled Darcy and Stokes equations
Christine Bernardi and Ajmia Younes OrfiComputers & Mathematics with Applications 76 (2) 340 (2018)
https://doi.org/10.1016/j.camwa.2018.04.021
A Mortar Method Using Nonconforming and Mixed Finite Elements for the Coupled Stokes-Darcy Model
Peiqi Huang, Jinru Chen and Mingchao CaiAdvances in Applied Mathematics and Mechanics 9 (3) 596 (2017)
https://doi.org/10.4208/aamm.2016.m1397
A posteriori error analysis of a fully-mixed formulation for the Brinkman–Darcy problem
M. Álvarez, G. N. Gatica and R. Ruiz-BaierCalcolo 54 (4) 1491 (2017)
https://doi.org/10.1007/s10092-017-0238-z
A multiscale flux basis for mortar mixed discretizations of Stokes–Darcy flows
Benjamin Ganis, Danail Vassilev, ChangQing Wang and Ivan YotovComputer Methods in Applied Mechanics and Engineering 313 259 (2017)
https://doi.org/10.1016/j.cma.2016.09.037
A Uniformly Stable Nonconforming FEM Based on Weighted Interior Penalties for Darcy-Stokes-Brinkman Equations
Peiqi Huang and Zhilin LiNumerical Mathematics: Theory, Methods and Applications 10 (1) 22 (2017)
https://doi.org/10.4208/nmtma.2017.m1610
Spectral discretization of Darcy equations coupled with Stokes equations by vorticity-velocity-pressure formulations
Yassine Mabrouki, Saloua Mani Aouadi and Jamil SatouriNumerical Methods for Partial Differential Equations 33 (5) 1628 (2017)
https://doi.org/10.1002/num.22157
Analysis of a Navier–Stokes–Darcy coupling problem
Yassine Mabrouki and Jamil SatouriAdvances in Pure and Applied Mathematics 7 (3) 177 (2016)
https://doi.org/10.1515/apam-2016-0017
Weak Galerkin method for the coupled Darcy–Stokes flow
Wenbin Chen, Fang Wang and Yanqiu WangIMA Journal of Numerical Analysis 36 (2) 897 (2016)
https://doi.org/10.1093/imanum/drv012
A priori error analysis of the fully discretized time-dependent coupled Darcy and Stokes equations
Christine Bernardi and Ajmia Younes OrfiSeMA Journal 73 (2) 97 (2016)
https://doi.org/10.1007/s40324-015-0058-5
A posteriori error analysis for Navier–Stokes equations coupled with Darcy problem
M. L. Hadji, A. Assala and F. Z. NouriCalcolo 52 (4) 559 (2015)
https://doi.org/10.1007/s10092-014-0130-z
Mortar multiscale finite element methods for Stokes–Darcy flows
Vivette Girault, Danail Vassilev and Ivan YotovNumerische Mathematik 127 (1) 93 (2014)
https://doi.org/10.1007/s00211-013-0583-z
Parallel, non-iterative, multi-physics domain decomposition methods for time-dependent Stokes-Darcy systems
Yanzhao Cao, Max Gunzburger, Xiaoming He and Xiaoming WangMathematics of Computation 83 (288) 1617 (2014)
https://doi.org/10.1090/S0025-5718-2014-02779-8
Approximation of the Stokes–Darcy System by Optimization
V. J. Ervin, E. W. Jenkins and Hyesuk LeeJournal of Scientific Computing 59 (3) 775 (2014)
https://doi.org/10.1007/s10915-013-9779-8
Least squares approach for the time-dependent nonlinear Stokes–Darcy flow
Hyesuk Lee and Kelsey RifeComputers & Mathematics with Applications 67 (10) 1806 (2014)
https://doi.org/10.1016/j.camwa.2014.04.002
Domain Decomposition Methods in Science and Engineering XXI
Géraldine Pichot, Baptiste Poirriez, Jocelyne Erhel and Jean-Raynald de DreuzyLecture Notes in Computational Science and Engineering, Domain Decomposition Methods in Science and Engineering XXI 98 99 (2014)
https://doi.org/10.1007/978-3-319-05789-7_8
Decoupling the Stationary Navier-Stokes-Darcy System with the Beavers-Joseph-Saffman Interface Condition
Yong Cao, Yuchuan Chu, Xiaoming He and Mingzhen WeiAbstract and Applied Analysis 2013 1 (2013)
https://doi.org/10.1155/2013/136483
Some low order nonconforming mixed finite elements combined with Raviart–Thomas elements for a coupled Stokes–Darcy model
Peiqi Huang and Jinru ChenJapan Journal of Industrial and Applied Mathematics 30 (3) 565 (2013)
https://doi.org/10.1007/s13160-013-0119-z
Robust a Posteriori Error Control and Adaptivity for Multiscale, Multinumerics, and Mortar Coupling
Gergina V. Pencheva, Martin Vohralík, Mary F. Wheeler and Tim WildeySIAM Journal on Numerical Analysis 51 (1) 526 (2013)
https://doi.org/10.1137/110839047
Adjoint Based A Posteriori Analysis of Multiscale Mortar Discretizations with Multinumerics
Simon Tavener and Tim WildeySIAM Journal on Scientific Computing 35 (6) A2621 (2013)
https://doi.org/10.1137/12089973X
A nonconforming rectangular finite element pair for the Darcy–Stokes–Brinkman model
Ruisheng Qi and Xiaoyuan YangNumerical Methods for Partial Differential Equations 29 (2) 510 (2013)
https://doi.org/10.1002/num.21718
A Mixed and Nonconforming FEM with Nonmatching Meshes for a Coupled Stokes-Darcy Model
Peiqi Huang, Jinru Chen and Mingchao CaiJournal of Scientific Computing 53 (2) 377 (2012)
https://doi.org/10.1007/s10915-012-9574-y
Non-iterative domain decomposition methods for a non-stationary Stokes–Darcy model with Beavers–Joseph interface condition
Wenqiang Feng, Xiaoming He, Zhu Wang and Xu ZhangApplied Mathematics and Computation 219 (2) 453 (2012)
https://doi.org/10.1016/j.amc.2012.05.012
A residual-based a posteriori error estimator for a fully-mixed formulation of the Stokes–Darcy coupled problem
Gabriel N. Gatica, Ricardo Oyarzúa and Francisco-Javier SayasComputer Methods in Applied Mechanics and Engineering 200 (21-22) 1877 (2011)
https://doi.org/10.1016/j.cma.2011.02.009
Robin–Robin domain decomposition methods for the steady-state Stokes–Darcy system with the Beavers–Joseph interface condition
Yanzhao Cao, Max Gunzburger, Xiaoming He and Xiaoming WangNumerische Mathematik 117 (4) 601 (2011)
https://doi.org/10.1007/s00211-011-0361-8
A Symmetric Nodal Conservative Finite Element Method for the Darcy Equation
Gabriel R. Barrenechea, Leopoldo P. Franca and Frédéric ValentinSIAM Journal on Numerical Analysis 47 (5) 3652 (2009)
https://doi.org/10.1137/080724381
A Finite Element Method Based on Weighted Interior Penalties for Heterogeneous Incompressible Flows
Carlo D'Angelo and Paolo ZuninoSIAM Journal on Numerical Analysis 47 (5) 3990 (2009)
https://doi.org/10.1137/080726318
DISCRETIZATION OF AN UNSTEADY FLOW THROUGH A POROUS SOLID MODELED BY DARCY'S EQUATIONS
CHRISTINE BERNARDI, VIVETTE GIRAULT and KUMBAKONAM R. RAJAGOPALMathematical Models and Methods in Applied Sciences 18 (12) 2087 (2008)
https://doi.org/10.1142/S0218202508003303