Analysis of linear and quadratic simplicial finite volume methods for elliptic equations

Jinchao Xu, Qingsong Zou

Research output: Contribution to journalArticle

90 Citations (Scopus)

Abstract

This paper is devoted to analysis of some convergent properties of both linear and quadratic simplicial finite volume methods (FVMs) for elliptic equations. For linear FVM on domains in any dimensions, the inf-sup condition is established in a simple fashion. It is also proved that the solution of a linear FVM is super-close to that of a relevant finite element method (FEM). As a result, some a posterior error estimates and also algebraic solvers for FEM are extended to FVM. For quadratic FVM on domains in two dimensions, the inf-sup condition is established under some weak condition on the grid.

Original languageEnglish (US)
Pages (from-to)469-492
Number of pages24
JournalNumerische Mathematik
Volume111
Issue number3
DOIs
StatePublished - Jan 1 2009

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Finite volume method
Finite Volume Method
Elliptic Equations
Inf-sup Condition
Finite Element Method
Finite element method
Error Estimates
Two Dimensions
Grid

All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Applied Mathematics

Cite this

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Analysis of linear and quadratic simplicial finite volume methods for elliptic equations. / Xu, Jinchao; Zou, Qingsong.

In: Numerische Mathematik, Vol. 111, No. 3, 01.01.2009, p. 469-492.

Research output: Contribution to journalArticle

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