Coupling Darcy and Stokes equations for porous media with cracks
ESAIM: M2AN, 39 1 (2005) 7-35
Published online: 2005-03-15
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 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
Spectral discretization of the time‐dependent vorticity–velocity–pressure formulation of the Stokes problem
Mohamed Abdelwahed and Nejmeddine ChorfiMathematical Methods in the Applied Sciences 47 (13) 10624 (2024)
https://doi.org/10.1002/mma.6353
Spectral element discretization of the time-dependent Stokes problem with nonstandard boundary conditions
Mohamed Abdelwahed and Nejmeddine ChorfiBoundary Value Problems 2024 (1) (2024)
https://doi.org/10.1186/s13661-023-01815-1
2083 (2023)
https://doi.org/10.1007/978-981-99-1964-2_178
Least‐squares formulations for Stokes equations with non‐standard boundary conditions—A unified approach
S. Mohapatra, N. Kishore Kumar and Shivangi JoshiMathematical Methods in the Applied Sciences 46 (16) 16463 (2023)
https://doi.org/10.1002/mma.9271
Model adaptation for non-linear elliptic equations in mixed form: existence of solutions and numerical strategies
Alessio Fumagalli and Francesco Saverio PatacchiniESAIM: Mathematical Modelling and Numerical Analysis 56 (2) 565 (2022)
https://doi.org/10.1051/m2an/2022016
An analysis on the penalty and Nitsche's methods for the Stokes–Darcy system with a curved interface
Guanyu Zhou, Takahito Kashiwabara, Issei Oikawa, Eric Chung and Ming-Cheng ShiueApplied Numerical Mathematics 165 83 (2021)
https://doi.org/10.1016/j.apnum.2021.02.006
Computation of macroscopic permeability of doubly porous media with FFT based numerical homogenization method
Sarra Mezhoud, Vincent Monchiet, Michel Bornert and Daniel GrandeEuropean Journal of Mechanics - B/Fluids 83 141 (2020)
https://doi.org/10.1016/j.euromechflu.2020.04.012
Macroscopic permeability of doubly porous solids with spheroidal macropores: closed-form approximate solutions of the longitudinal permeability
Vincent monchietProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476 (2244) (2020)
https://doi.org/10.1098/rspa.2020.0224
Stokes Flow Past Porous Bodies of Arbitrary Shape
R. Radha and B. Sri PadmavatiIndian Journal of Pure and Applied Mathematics 51 (3) 1247 (2020)
https://doi.org/10.1007/s13226-020-0462-0
Some DG schemes for the Stokes–Darcy problem using P1/P1 element
Guanyu Zhou, Takahito Kashiwabara, Issei Oikawa, Eric Chung and Ming-Cheng ShiueJapan Journal of Industrial and Applied Mathematics 36 (3) 1101 (2019)
https://doi.org/10.1007/s13160-019-00377-z
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
11539 60 (2019)
https://doi.org/10.1007/978-3-030-22747-0_5
Vorticity‐pressure formulations for the Brinkman‐Darcy coupled problem
Verónica Anaya, David Mora, Carlos Reales and Ricardo Ruiz‐BaierNumerical Methods for Partial Differential Equations 35 (2) 528 (2019)
https://doi.org/10.1002/num.22312
Penalty method with Crouzeix–Raviart approximation for the Stokes equations under slip boundary condition
Takahito Kashiwabara, Issei Oikawa and Guanyu ZhouESAIM: Mathematical Modelling and Numerical Analysis 53 (3) 869 (2019)
https://doi.org/10.1051/m2an/2019008
On the Shape Differentiability of Objectives: A Lagrangian Approach and the Brinkman Problem
José Rodrigo González Granada, Joachim Gwinner and Victor A. KovtunenkoAxioms 7 (4) 76 (2018)
https://doi.org/10.3390/axioms7040076
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 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
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 the HDG method for the stokes–darcy coupling
Gabriel N. Gatica and Filánder A. SequeiraNumerical Methods for Partial Differential Equations 33 (3) 885 (2017)
https://doi.org/10.1002/num.22128
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 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 primal-mixed formulation for the strong coupling of quasi-Newtonian fluids with porous media
Sebastián Domínguez, Gabriel N. Gatica, Antonio Márquez and Salim MeddahiAdvances in Computational Mathematics 42 (3) 675 (2016)
https://doi.org/10.1007/s10444-015-9439-7
A vorticity-based fully-mixed formulation for the 3D Brinkman–Darcy problem
Mario Alvarez, Gabriel N. Gatica and Ricardo Ruiz-BaierComputer Methods in Applied Mechanics and Engineering 307 68 (2016)
https://doi.org/10.1016/j.cma.2016.04.017
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
New fully-mixed finite element methods for the Stokes–Darcy coupling
Jessika Camaño, Gabriel N. Gatica, Ricardo Oyarzúa, Ricardo Ruiz-Baier and Pablo VenegasComputer Methods in Applied Mechanics and Engineering 295 362 (2015)
https://doi.org/10.1016/j.cma.2015.07.007
Analysis of an augmented fully-mixed approach for the coupling of quasi-Newtonian fluids and porous media
Gabriel N. Gatica, Antonio Márquez, Ricardo Oyarzúa and Ramiro RebolledoComputer Methods in Applied Mechanics and Engineering 270 76 (2014)
https://doi.org/10.1016/j.cma.2013.11.017
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
Error studies of the Coupling Darcy-Stokes System with velocity-pressure formulation
Fida El Chami, Gihane Mansour and Toni SayahCalcolo 49 (2) 73 (2012)
https://doi.org/10.1007/s10092-011-0046-9
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 Parallel Robin–Robin Domain Decomposition Method for the Stokes–Darcy System
Wenbin Chen, Max Gunzburger, Fei Hua and Xiaoming WangSIAM Journal on Numerical Analysis 49 (3) 1064 (2011)
https://doi.org/10.1137/080740556
Analysis of fully-mixed finite element methods for the Stokes-Darcy coupled problem
Gabriel Gatica, Ricardo Oyarzúa and Francisco-Javier SayasMathematics of Computation 80 (276) 1911 (2011)
https://doi.org/10.1090/S0025-5718-2011-02466-X
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
Convergence of a family of Galerkin discretizations for the Stokes-Darcy coupled problem
Gabriel N. Gatica, Ricardo Oyarzúa and Francisco-Javier SayasNumerical Methods for Partial Differential Equations 27 (3) 721 (2011)
https://doi.org/10.1002/num.20548
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
Spectral Discretization of the Axisymmetric Vorticity, Velocity and Pressure Formulation of the Stokes Problem
Nehla Abdellatif, Nejmeddine Chorfi and Sihem TrabelsiJournal of Scientific Computing 47 (3) 419 (2011)
https://doi.org/10.1007/s10915-010-9446-2
A theoretical treatment on the mechanics of interfaces in deformable porous media
Franck J. VernereyInternational Journal of Solids and Structures 48 (22-23) 3129 (2011)
https://doi.org/10.1016/j.ijsolstr.2011.07.005
A Residual-Based A Posteriori Error Estimator for the Stokes–Darcy Coupled Problem
Ivo Babuška and Gabriel N. GaticaSIAM Journal on Numerical Analysis 48 (2) 498 (2010)
https://doi.org/10.1137/080727646
Coupling of Darcy–Forchheimer and Compressible Navier–Stokes Equations with Heat Transfer
M. Amara, D. Capatina and L. LizaikSIAM Journal on Scientific Computing 31 (2) 1470 (2009)
https://doi.org/10.1137/070709517
Mortar finite element discretization of a model coupling Darcy and Stokes equations
Christine Bernardi, Tomás Chacón Rebollo, Frédéric Hecht and Zoubida MghazliESAIM: Mathematical Modelling and Numerical Analysis 42 (3) 375 (2008)
https://doi.org/10.1051/m2an:2008009
Spectral Discretization of the Vorticity, Velocity, and Pressure Formulation of the Stokes Problem
Christine Bernardi and Nejmeddine ChorfiSIAM Journal on Numerical Analysis 44 (2) 826 (2006)
https://doi.org/10.1137/050622687