A UNIFIED APPROACH TO MIMETIC FINITE DIFFERENCE, HYBRID FINITE VOLUME AND MIXED FINITE VOLUME METHODS

Keywords

Finite volume method, Finite element method, Mathematics, Regular grid, Polygon mesh

References

• A FAMILY OF MIMETIC FINITE DIFFERENCE METHODS ON POLYGONAL AND POLYHEDRAL MESHESFranco Brezzi, Konstantin Lipnikov, Valeria Simoncini — 2005
• Finite volume schemes for elliptic and elliptic-hyperbolic problems on triangular meshesRaphae`le Herbin, Olivier Labergerie — 1997
• Study of the mixed finite volume method for Stokes and Navier‐Stokes equationsJérôme Droniou, Robert Eymard — 2009
• A new finite volume scheme for anisotropic diffusion problems on general grids: convergence analysisRobert Eymard, Thierry Gallouët, Raphaèle Herbin — 2007
• Convergence Analysis of a Mixed Finite Volume Scheme for an Elliptic-Parabolic System Modeling Miscible Fluid Flows in Porous MediaClaire Chainais-Hillairet, Jérôme Droniou — 2007
• Flux reconstruction and solution post-processing in mimetic finite difference methodsAndrea Cangiani, Gianmarco Manzini — 2008
• A Higher-Order Formulation of the Mimetic Finite Difference MethodL. Beirão da Veiga, Gianmarco Manzini — 2008
• Cell centred discretisation of non linear elliptic problems on general multidimensional polyhedral gridsRobert Eymard, Thierry Gallouët, Raphaèle Herbin — 2009
• CONVERGENCE OF MIMETIC FINITE DIFFERENCE METHOD FOR DIFFUSION PROBLEMS ON POLYHEDRAL MESHES WITH CURVED FACESFranco Brezzi, Konstantin Lipnikov, Mikhail Shashkov — 2006
• A mixed finite volume scheme for anisotropic diffusion problems on any gridJérôme Droniou, Robert Eymard — 2006
• The G method for heterogeneous anisotropic diffusion on general meshesLéo Agelas, Daniele A. Di Pietro, Jérôme Droniou — 2010
• Discrete functional analysis tools for Discontinuous Galerkin methods with application to the incompressible Navier-Stokes equationsDaniele A. Di Pietro, Alexandre Ern — 2010
• High-order mimetic finite difference method for diffusion problems on polygonal meshesVitaliy Gyrya, Konstantin Lipnikov — 2008
• Convergence of the Mimetic Finite Difference Method for Diffusion Problems on Polyhedral MeshesFranco Brezzi, Konstantin Lipnikov, Mikhail Shashkov — 2005
• A new discretization methodology for diffusion problems on generalized polyhedral meshesFranco Brezzi, Konstantin Lipnikov, Mikhail Shashkov — 2007
• The mimetic finite difference method on polygonal meshes for diffusion-type problemsYu. I. Kuznetsov, Konstantin Lipnikov, Mikhail Shashkov — 2004
• An a posteriori error estimator for the mimetic finite difference approximation of elliptic problemsL. Beirão da Veiga, Gianmarco Manzini — 2008
• Finite volume schemes for fully non-linear elliptic equations in divergence formJérôme Droniou — 2006
• An error estimate for a finite volume scheme for a diffusion–convection problem on a triangular meshRaphaèle Herbin — 1995
• A residual based error estimator for the Mimetic Finite Difference methodL. Beirão da Veiga — 2007

Cited by

• Schémas volumes finis sur maillages généraux en milieux hétérogènes anisotropes pour les écoulements polyphasiques en milieux poreuxCindy Guichard — 2011
• Problématiques d’analyse numérique et de modélisation pour écoulements de fluides environnementauxM. Cathala — 2013
• Gradient discretization of hybrid dimensional Darcy flows in fractured porous mediaKonstantin Brenner, Mayya Groza, Cindy Guichard — 2014
• Elaboration de solveurs volumes finis 2D/3D pour résoudre le problème de l'élasticité linéaireBenjamin Martin — 2012
• Construction et analyse numérique de schéma asymptotic preserving sur maillages non structurés. Application au transport linéaire et aux systèmes de FriedrichsEmmanuel Franck — 2012
• Compatible discrete operator schemes on polyhedral meshes for elliptic and Stokes equationsJérôme Bonelle — 2014
• Étude de schémas numériques pour les écoulements diphasiques en milieu poreux déformable pour des maillages quelconques : application au stockage de déchets radioactifsOphélie Angelini — 2010
• Arbitrary-order mixed methods for heterogeneous anisotropic diffusion on general meshesDaniele A. Di Pietro, Alexandre Ern — 2013
• Bridging the hybrid high-order and hybridizable discontinuous Galerkin methodsBernardo Cockburn, Daniele A. Di Pietro, Alexandre Ern — 2016
• ÉTUDE MATHÉMATIQUE ET NUMÉRIQUE DE MODÈLES EN CHIMIOTAXIE-FLUIDE ET APPLICATIONS À LA BIOLOGIEGeorges Chamoun — 2014
• A DSEL in C++ for lowest-order methods for diffusive problem on general meshesJean-Marc Gratien — 2013
• Uniform-in-time convergence of numerical methods for non-linear degenerate parabolic equationsJérôme Droniou, Robert Eymard — 2014
• Semi hybrid method for heterogeneous and anisotropic diffusion problems on general meshesJulien Coatléven — 2015
• Topics in structure-preserving discretization*Snorre H. Christiansen — 2010
• Tackling coupled problems in porous media : development of numerical models and an open source simulatorBernd Flemisch — 2013
• Numerical comparison of robustness of some reduction methods in rough gridsJiangyong Hou, Shuyu Sun, Zhangxin Chen — 2014
• H(div) and H(curl)-conforming VEML. Beirão da Veiga, Franco Brezzi, L. D. Marini — 2014
• Gradient schemes for two‐phase flow in heterogeneous porous media and Richards equationRobert Eymard, Cindy Guichard, Raphaèle Herbin — 2014
• A Review of Hybrid High-Order Methods: Formulations, Computational Aspects, Comparison with Other MethodsDaniele A. Di Pietro, Alexandre Ern, Simon Lemaire — 2016
• A Discontinuous-Skeletal Method for Advection-Diffusion-Reaction on General MeshesDaniele A. Di Pietro, Jérôme Droniou, Alexandre Ern — 2014

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