First-order convergence of multi-point flux approximation on triangular grids and comparison with mixed finite element methods
type: Item
instance of: scholarly article
title: First-order convergence of multi-point flux approximation on triangular grids and comparison with mixed finite element methods
zbMATH Open document ID: 1220.65152
author: Markus Bause
author: Joachim Hoffmann
author: Peter Knabner
published in: Numerische Mathematik
publication date: 2010-08-06T00:00:00Z
review text: The authors show first order convergence of a multi-point flux approximation (MPFA) control volume method on an unstructured triangular grid. A perturbed mixed finite element method with broken Raviart-Thomas elements and a specific quadrature rule is introduced and the equivalence of the MPFA method with a hybrid variant of the mixed method is proved. The theoretical error estimates are verified by numerical convergence studies. The accuracy of the MPFA approximation is carefully compared with that of a lowest order Raviart-Thomas and Brezzi-Douglas-Marini approach.
reviewed by: Ariadna Lucia Pletea
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 65N08
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65N50
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 5764625
zbMATH Keywords: multi-point flux approximation control volume methods
zbMATH Keywords: finite element
zbMATH Keywords: convergence
zbMATH Keywords: comparison of methods
zbMATH Keywords: numerical examples
zbMATH Keywords: triangular grid
zbMATH Keywords: Raviart-Thomas elements
zbMATH Keywords: error estimates
MaRDI profile type: Publication
full work available at URL: s00211-010-0290-y
OpenAlex ID: W2048802843
cites work: Discretization on Unstructured Grids for Inhomogeneous, Anisotropic Media. Part I: Derivation of the Methods
cites work: An introduction to multipoint flux approximations for quadrilateral grids
cites work: Convergence of the finite volume MPFA O scheme for heterogeneous anisotropic diffusion problems on general meshes
cites work: Q4864112
cites work: A Nonlinear Mixed Finite Element Method for a Degenerate Parabolic Equation Arising in Flow in Porous Media
cites work: Numerical Study of Mixed Finite Element and Multi Point Flux Approximation of Flow in Porous Media
cites work: Mixed and Hybrid Finite Element Methods
cites work: Suboptimal and Optimal Convergence in Mixed Finite Element Methods
cites work: Q3470840
cites work: Robust convergence of multi point flux approximation on rough grids
cites work: Convergence of MPFA on triangulations and for Richards' equation
cites work: Q3690482
cites work: Q4303980
cites work: Order of Convergence Estimates for an Euler Implicit, Mixed Finite Element Discretization of Richards' Equation
cites work: Q4169288
cites work: Equivalence between lowest-order mixed finite element and multi-point finite volume methods on simplicial meshes
cites work: A Multipoint Flux Mixed Finite Element Method
cites work: Q3760934
cites work: From mixed finite elements to finite volumes for elliptic PDEs in two and three dimensions
DOI: 10.1007/S00211-010-0290-Y
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description: scientific article; zbMATH DE number 5764625