The G method for heterogeneous anisotropic diffusion on general meshes
ESAIM: M2AN, 44 4 (2010) 597-625
Published online: 2010-03-17
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 nonlinear finite volume element method preserving the discrete maximum principle for heterogeneous anisotropic diffusion equations
Dan Wu, Junliang Lv and Zhiqiang ShengJournal of Computational and Applied Mathematics 451 116023 (2024)
https://doi.org/10.1016/j.cam.2024.116023
A mimetic interpolation-free cell-centered finite volume scheme for the 2D and 3D heterogeneous anisotropic diffusion equations
Shuai MiaoJournal of Computational and Applied Mathematics 443 115760 (2024)
https://doi.org/10.1016/j.cam.2024.115760
An interpolation-free cell-centered discretization of the heterogeneous and anisotropic diffusion problems on polygonal meshes
Shuai Miao, Jiming Wu and Yanzhong YaoComputers & Mathematics with Applications 130 105 (2023)
https://doi.org/10.1016/j.camwa.2022.11.023
A conservative network element method for diffusion-advection-reaction problems
Julien CoatlévenESAIM: Mathematical Modelling and Numerical Analysis 57 (4) 2007 (2023)
https://doi.org/10.1051/m2an/2023040
Unconditionally stable small stencil enriched multiple point flux approximations of heterogeneous diffusion problems on general meshes
Julien CoatlévenIMA Journal of Numerical Analysis (2023)
https://doi.org/10.1093/imanum/drad087
Error estimate of the cell-centered nonlinear positivity-preserving two-point flux approximation schemes
Lei Lin, Junliang Lv and Dan WuComputers & Mathematics with Applications 137 1 (2023)
https://doi.org/10.1016/j.camwa.2023.02.015
Convergence of nonlinear finite volume schemes for two-phase porous media flow on general meshes
Léo Agélas, Martin Schneider, Guillaume Enchéry and Bernd FlemischIMA Journal of Numerical Analysis 42 (1) 515 (2022)
https://doi.org/10.1093/imanum/draa064
A linearity-preserving technique for finite volume schemes of anisotropic diffusion problems on polygonal meshes
Cheng Dong and Tong KangMathematics and Computers in Simulation 201 141 (2022)
https://doi.org/10.1016/j.matcom.2022.05.011
A network element method for heterogeneous and anisotropic diffusion-reaction problems
Julien CoatlévenJournal of Computational Physics 470 111597 (2022)
https://doi.org/10.1016/j.jcp.2022.111597
First-order Continuation Method for Steady-State Variably Saturated Groundwater Flow Modeling
D. V. AnuprienkoLobachevskii Journal of Mathematics 43 (4) 924 (2022)
https://doi.org/10.1134/S199508022207006X
Analysis of the decoupled and positivity-preserving DDFV schemes for diffusion problems on polygonal meshes
Qiannan Dong, Shuai Su and Jiming WuAdvances in Computational Mathematics 46 (2) (2020)
https://doi.org/10.1007/s10444-020-09748-4
A hybrid-dimensional discrete fracture model for non-isothermal two-phase flow in fractured porous media
Dennis Gläser, Bernd Flemisch, Rainer Helmig and Holger ClassGEM - International Journal on Geomathematics 10 (1) (2019)
https://doi.org/10.1007/s13137-019-0116-8
A third Strang lemma and an Aubin–Nitsche trick for schemes in fully discrete formulation
Daniele A. Di Pietro and Jérôme DroniouCalcolo 55 (3) (2018)
https://doi.org/10.1007/s10092-018-0282-3
Comparison of finite-volume schemes for diffusion problems
Martin Schneider, Dennis Gläser, Bernd Flemisch, et al.Oil & Gas Science and Technology – Revue d’IFP Energies nouvelles 73 82 (2018)
https://doi.org/10.2516/ogst/2018064
Finite Volumes for Complex Applications VIII - Methods and Theoretical Aspects
J. Droniou and R. EymardSpringer Proceedings in Mathematics & Statistics, Finite Volumes for Complex Applications VIII - Methods and Theoretical Aspects 199 311 (2017)
https://doi.org/10.1007/978-3-319-57397-7_24
Cell-centered nonlinear finite-volume methods for the heterogeneous anisotropic diffusion problem
Kirill M. Terekhov, Bradley T. Mallison and Hamdi A. TchelepiJournal of Computational Physics 330 245 (2017)
https://doi.org/10.1016/j.jcp.2016.11.010
1 (2017)
https://doi.org/10.1002/9781119176817.ecm2010
A virtual volume method for heterogeneous and anisotropic diffusion-reaction problems on general meshes
Julien CoatlévenESAIM: Mathematical Modelling and Numerical Analysis 51 (3) 797 (2017)
https://doi.org/10.1051/m2an/2016036
ArcFVDSL, a DSEL Combined to HARTS, a Runtime System Layer to Implement Efficient Numerical Methods to Solve Diffusive Problems on New Heterogeneous Hardware Architecture
Jean-Marc Gratien and S. de ChaisemartinOil & Gas Science and Technology – Revue d’IFP Energies nouvelles 72 (2) 12 (2017)
https://doi.org/10.2516/ogst/2017007
Convergence of nonlinear finite volume schemes for heterogeneous anisotropic diffusion on general meshes
Martin Schneider, Léo Agélas, Guillaume Enchéry and Bernd FlemischJournal of Computational Physics 351 80 (2017)
https://doi.org/10.1016/j.jcp.2017.09.003
A two-step finite volume method to discretize heterogeneous and anisotropic pressure equation on general grids
Wenjuan Zhang and Mohammed Al KobaisiAdvances in Water Resources 108 231 (2017)
https://doi.org/10.1016/j.advwatres.2017.08.008
Modeling anisotropic flow and heat transport by using mimetic finite differences
Tao Chen, Christoph Clauser, Gabriele Marquart, Karen Willbrand and Henrik BüsingAdvances in Water Resources 94 441 (2016)
https://doi.org/10.1016/j.advwatres.2016.06.006
Semi hybrid method for heterogeneous and anisotropic diffusion problems on general meshes
Julien CoatlévenESAIM: Mathematical Modelling and Numerical Analysis 49 (4) 1063 (2015)
https://doi.org/10.1051/m2an/2015005
A Review of Recent Advances in Discretization Methods,a PosterioriError Analysis, and Adaptive Algorithms for Numerical Modeling in Geosciences
Daniele A. Di Pietro and Martin VohralíkOil & Gas Science and Technology – Revue d’IFP Energies nouvelles 69 (4) 701 (2014)
https://doi.org/10.2516/ogst/2013158
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 YousefComputers & Mathematics with Applications 68 (12) 2331 (2014)
https://doi.org/10.1016/j.camwa.2014.08.008
Finite-difference schemes for anisotropic diffusion
Bram van Es, Barry Koren and Hugo J. de BlankJournal of Computational Physics 272 526 (2014)
https://doi.org/10.1016/j.jcp.2014.04.046
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 YousefJournal of Computational Physics 276 163 (2014)
https://doi.org/10.1016/j.jcp.2014.06.061
Finite volume schemes for diffusion equations: Introduction to and review of modern methods
Jerome DroniouMathematical Models and Methods in Applied Sciences 24 (08) 1575 (2014)
https://doi.org/10.1142/S0218202514400041
Numerical comparison of robustness of some reduction methods in rough grids
Jiangyong Hou, Shuyu Sun and Zhangxin ChenNumerical Methods for Partial Differential Equations 30 (5) 1484 (2014)
https://doi.org/10.1002/num.21873
Carleman Estimates for Some Non-Smooth Anisotropic Media
Assia Benabdallah, Yves Dermenjian and Laetitia ThevenetCommunications in Partial Differential Equations 38 (10) 1763 (2013)
https://doi.org/10.1080/03605302.2013.804552
MIXED FINITE ELEMENT METHODS: IMPLEMENTATION WITH ONE UNKNOWN PER ELEMENT, LOCAL FLUX EXPRESSIONS, POSITIVITY, POLYGONAL MESHES, AND RELATIONS TO OTHER METHODS
MARTIN VOHRALÍK and BARBARA I. WOHLMUTHMathematical Models and Methods in Applied Sciences 23 (05) 803 (2013)
https://doi.org/10.1142/S0218202512500613
On the conservativity of cell-centered Galerkin methods
Daniele A. Di PietroComptes Rendus. Mathématique 351 (3-4) 155 (2013)
https://doi.org/10.1016/j.crma.2013.03.001
A domain-specific embedded language in C++ for lowest-order discretizations of diffusive problems on general meshes
Daniele A. Di Pietro, Jean-Marc Gratien and Christophe Prud’hommeBIT Numerical Mathematics 53 (1) 111 (2013)
https://doi.org/10.1007/s10543-012-0403-3
Modelling and Simulation in Fluid Dynamics in Porous Media
J.-M. GratienSpringer Proceedings in Mathematics & Statistics, Modelling and Simulation in Fluid Dynamics in Porous Media 28 157 (2013)
https://doi.org/10.1007/978-1-4614-5055-9_10
Vertex-centred discretization of multiphase compositional Darcy flows on general meshes
Robert Eymard, Cindy Guichard, Raphaele Herbin and Roland MassonComputational Geosciences 16 (4) 987 (2012)
https://doi.org/10.1007/s10596-012-9299-x
Cell centered Galerkin methods for diffusive problems
Daniele A. Di PietroESAIM: Mathematical Modelling and Numerical Analysis 46 (1) 111 (2012)
https://doi.org/10.1051/m2an/2011016
Construction and Convergence Study of Schemes Preserving the Elliptic Local Maximum Principle
Jérôme Droniou and Christophe Le PotierSIAM Journal on Numerical Analysis 49 (2) 459 (2011)
https://doi.org/10.1137/090770849
Finite Volumes for Complex Applications VI Problems & Perspectives
Daniele A. Di Pietro and Jean-Marc GratienSpringer Proceedings in Mathematics, Finite Volumes for Complex Applications VI Problems & Perspectives 4 803 (2011)
https://doi.org/10.1007/978-3-642-20671-9_84
Correction non linéaire et principe du maximum pour la discrétisation d'opérateurs de diffusion avec des schémas volumes finis centrés sur les mailles
Christophe Le PotierComptes Rendus. Mathématique 348 (11-12) 691 (2010)
https://doi.org/10.1016/j.crma.2010.04.017
A compact cell-centered Galerkin method with subgrid stabilization
Daniele A. Di PietroComptes Rendus. Mathématique 349 (1-2) 93 (2010)
https://doi.org/10.1016/j.crma.2010.11.017