On the finite volume element version of Ritz-Volterra projection and applications to related equations

Tie Zhang, Yanping Lin, Robert J. Tait

Research output: Journal article publicationJournal articleAcademic researchpeer-review

11 Citations (Scopus)

Abstract

We present a general error analysis frqmework for the finite volume element (FVE) approximation to the Ritz-Volterra projection, the Sobolev equations and parabolic integro-differential equations. The main idea in our paper is to consider the FVE methods as perturbations of standard finite element methods which enables us to derive the optimal L2 and H1 norm error estimates, and the L∞ and W∞1 norm error estimates by means of the time dependent Green functions. Our discussions also include elliptic and parabolic problems as the special cases.
Original languageEnglish
Pages (from-to)491-504
Number of pages14
JournalJournal of Computational Mathematics
Volume20
Issue number5
Publication statusPublished - 1 Sep 2002
Externally publishedYes

Keywords

  • Error analysis
  • Finite volume element
  • Integro-differential equations
  • Ritz-Volterra projection

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics
  • Computational Mathematics

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