On the finite volume element method
type: Item
instance of: scholarly article
title: On the finite volume element method
zbMATH Open document ID: 0731.65093
DOI: 10.1007/BF01385651
published in: Numerische Mathematik
publication date: 1991-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/133527
review text: The author considers the problem \(-\nabla \cdot (A\nabla u)=f\) on a polygonal domain \(\Omega \subset {\mathbb{R}}^ 2\) with \(u=0\) on \(\Gamma_ 0\), \(A\nabla u\cdot n=g\) on \(\Gamma_ 1\), \(\Gamma_ 0\cup \Gamma_ 1=\partial \Omega\), A uniformly elliptic. The author considers piecewise linear functions v on a regular triangularization of \(\Omega\), \(b_{ij}(v)=-\int_{\gamma_{ij}}(A\nabla v)\cdot n_{ij} ds\) for \(\gamma_{ij}\) an edge connecting triangle interior points (consistently taken as either circumcenters, orthocenters, incenters, or centroids), and the linear operator B defined by \((Bv)_ i=\sum_{j}b_{ij}(v).\) He gives conditions under which B will be uniformly elliptic, and under those conditions derives estimates on the discretization error.
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 4209517
zbMATH Keywords: finite volume method
zbMATH Keywords: finite elements
zbMATH Keywords: error estimates
zbMATH Keywords: finite volume element method
author: Zhiqiang Cai
reviewed by: James R. Kuttler
MaRDI profile type: Publication
cites work: Q4073917
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description: scientific article; zbMATH DE number 4209517