A symmetric finite volume scheme for selfadjoint elliptic problems
type: Item
instance of: scholarly article
title: A symmetric finite volume scheme for selfadjoint elliptic problems
zbMATH Open document ID: 1027.65150
DOI: 10.1016/S0377-0427(02)00428-4
author: Shengde Liang
author: Xiuling Ma
author: Aihui Zhou
published in: Journal of Computational and Applied Mathematics
publication date: 2003-02-23T00:00:00Z
review text: The authors introduce a new symmetric finite volume scheme for a general self-adjoint elliptic boundary value problem. Some relations between finite volume methods and finite difference methods are discussed. Some error estimates are provided for the \(L^2\)-norm, \(H^1\)-norm and \(L^{\infty}\)-norm. Furthermore, post-processing techniques are presented. Finally, some numerical results are performed on two academic cases.
reviewed by: X. Antoine
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 65N15
zbMATH DE Number: 1872847
zbMATH Keywords: finite element
zbMATH Keywords: finite volume
zbMATH Keywords: post processing
zbMATH Keywords: symmetric scheme
zbMATH Keywords: comparison of methods
zbMATH Keywords: numerical examples
zbMATH Keywords: error estimate
MaRDI profile type: Publication
cites work: Equivalent Norms for Sobolev Spaces
cites work: Some Error Estimates for the Box Method
cites work: On the finite volume element method
cites work: The Finite Volume Element Method for Diffusion Equations on General Triangulations
cites work: Error estimates in $L^2$, $H^1$ and $L^\infty$ in covolume methods for elliptic and parabolic problems: A unified approach
cites work: Q3890207
cites work: Finite volume element approximations of nonlocal reactive flows in porous media
cites work: Local Refinement Techniques for Elliptic Problems on Cell-Centered Grids I. Error Analysis
cites work: On first and second order box schemes
cites work: Q3745201
cites work: Asymptotically exact a posteriori estimators for the pointwise gradient error on each element in irregular meshes. I: A smooth problem and globally quasi-uniform meshes
cites work: On the Finite Volume Element Method for General Self-Adjoint Elliptic Problems
cites work: On superconvergence techniques
cites work: Q4238903
cites work: Some Optimal Error Estimates for Piecewise Linear Finite Element Approximations
cites work: Gradient recovery type a posteriori error estimates for finite element approximations on irregular meshes
cites work: The full approximation accuracy for the stream function-vorticity- pressure method
cites work: The superconvergent patch recovery anda posteriori error estimates. Part 1: The recovery technique
description: scientific article; zbMATH DE number 1872847