An a posteriori error estimator for the mimetic finite difference approximation of elliptic problems

Keywords

Polygon mesh, Estimator, A priori and a posteriori, Mathematics, Finite element method

References

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• The Mathematical Theory of Finite Element MethodsSusanne C. Brenner, L. Ridgway Scott — 1994
• The Orthogonal Decomposition Theorems for Mimetic Finite Difference MethodsJames M. Hyman, Mikhail Shashkov — 1999
• A FAMILY OF MIMETIC FINITE DIFFERENCE METHODS ON POLYGONAL AND POLYHEDRAL MESHESFranco Brezzi, Konstantin Lipnikov, Valeria Simoncini — 2005
• Lectures on Elliptic Boundary Value ProblemsShmuel Agmon — 1965
• Superconvergence of the Velocity in Mimetic Finite Difference Methods on QuadrilateralsMarkus Berndt, Konstantin Lipnikov, Mikhail Shashkov — 2005
• A posteriori error estimate for the mixed finite element methodCarsten Carstensen — 1997
• Flux reconstruction and solution post-processing in mimetic finite difference methodsAndrea Cangiani, Gianmarco Manzini — 2008
• CONVERGENCE OF MIMETIC FINITE DIFFERENCE METHOD FOR DIFFUSION PROBLEMS ON POLYHEDRAL MESHES WITH CURVED FACESFranco Brezzi, Konstantin Lipnikov, Mikhail Shashkov — 2006
• Convergence of mimetic finite difference discretizations of the diffusion equationMarkus Berndt, Konstantin Lipnikov, D. Moulton — 2001
• Mimetic Finite Difference Methods for Maxwell's Equations and the Equations of Magnetic Diffusion - AbstractJames M. Hyman, Mikhail Shashkov — 2001
• Approximation of boundary conditions for mimetic finite-difference methodsJames M. Hyman, Mikhail Shashkov — 1998
• A tensor artificial viscosity using a mimetic finite difference algorithmJ. Campbell, Mikhail Shashkov — 2001
• A Posteriori Error Estimates for Lowest-Order Mixed Finite Element Discretizations of Convection-Diffusion-Reaction EquationsMartin Vohralı́k — 2007
• Energy norm a posteriori error estimates for mixed finite element methodsCarlo Lovadina, Rolf Stenberg — 2006
• Adjoint operators for the natural discretizations of the divergence gradient and curl on logically rectangular gridsJames M. Hyman, Mikhail Shashkov — 1997
• The finite element method for elliptic problemsPhilippe G. Ciarlet — 2002
• Convergence of the Mimetic Finite Difference Method for Diffusion Problems on Polyhedral MeshesFranco Brezzi, Konstantin Lipnikov, Mikhail Shashkov — 2005
• A FINITE VOLUME METHOD FOR THE LAPLACE EQUATION ON ALMOST ARBITRARY TWO-DIMENSIONAL GRIDSKomla Domelevo, Pascal Omnès — 2005
• A new discretization methodology for diffusion problems on generalized polyhedral meshesFranco Brezzi, Konstantin Lipnikov, Mikhail Shashkov — 2007

Cited by

• A local error estimator for the mimetic finite diference methodH. Beirão da Veiga — 2008
• Post processing of solution and flux for the nodal mimetic finite difference methodL. Beirão da Veiga, Gianmarco Manzini, Mario Putti — 2015
• A mimetic discretization of the Reissner–Mindlin plate bending problemL. Beirão da Veiga, David Mora — 2011
• Mimetic finite difference methodKonstantin Lipnikov, Gianmarco Manzini, Mikhail Shashkov — 2014
• A high-order mimetic method on unstructured polyhedral meshes for the diffusion equationKonstantin Lipnikov, Gianmarco Manzini — 2014
• M-Adaptation in the mimetic finite difference methodVitaliy Gyrya, Konstantin Lipnikov, Gianmarco Manzini — 2014
• A mimetic discretization of elliptic obstacle problemsPaola F. Antonietti, L. Beirão da Veiga, Marco Verani — 2013
• New perspectives on polygonal and polyhedral finite element methodsGianmarco Manzini, A. Russo, N. Sukumar — 2014
• Arbitrary-Order Nodal Mimetic Discretizations of Elliptic Problems on Polygonal MeshesL. Beirão da Veiga, Konstantin Lipnikov, Gianmarco Manzini — 2011
• A Higher-Order Formulation of the Mimetic Finite Difference MethodL. Beirão da Veiga, Gianmarco Manzini — 2008
• Analysis of the monotonicity conditions in the mimetic finite difference method for elliptic problemsKonstantin Lipnikov, Gianmarco Manzini, D. Svyatskiy — 2011
• Residual a posteriori error estimation for the Virtual Element Method for elliptic problemsL. Beirão da Veiga, Gianmarco Manzini — 2015
• Convergence of the mimetic finite difference method for eigenvalue problems in mixed formAndrea Cangiani, Francesca Gardini, Gianmarco Manzini — 2011
• Mimetic scalar products of discrete differential formsFranco Brezzi, Annalisa Buffa, Gianmarco Manzini — 2014
• Error Analysis for a Mimetic Discretization of the Steady Stokes Problem on Polyhedral MeshesL. Beirão da Veiga, Konstantin Lipnikov, Gianmarco Manzini — 2010
• Mimetic finite differences for nonlinear and control problemsPaola F. Antonietti, L. Beirão da Veiga, Nadia Bigoni — 2014
• Mimetic Discretizations of Elliptic Control ProblemsPaola F. Antonietti, Nadia Bigoni, Marco Verani — 2013
• Virtual Elements for Linear Elasticity ProblemsL. Beirão da Veiga, Franco Brezzi, L. D. Marini — 2013
• The mimetic finite difference method for the 3D magnetostatic field problems on polyhedral meshesKonstantin Lipnikov, Gianmarco Manzini, Franco Brezzi — 2011
• FINITE VOLUME SCHEMES FOR DIFFUSION EQUATIONS: INTRODUCTION TO AND REVIEW OF MODERN METHODSJerome Droniou — 2014

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