On the accuracy of the finite volume element method based on piecewise linear polynomials

Richard E. Ewing, Tao Lin, Yanping Lin

Research output: Journal article publicationJournal articleAcademic researchpeer-review

217 Citations (Scopus)

Abstract

We present a general error estimation framework for a finite volume element (FVE) method based on linear polynomials for solving second-order elliptic boundary value problems. This framework treats the FVE method as a perturbation of the Galerkin finite element method and reveals that regularities in both the exact solution and the source term can affect the accuracy of FVE methods. In particular, the error estimates and counterexamples in this paper will confirm that the FVE method cannot have the standard O(h2) convergence rate in the L2 norm when the source term has the minimum regularity, only being in L2, even if the exact solution is in H2.
Original languageEnglish
Pages (from-to)1865-1888
Number of pages24
JournalSIAM Journal on Numerical Analysis
Volume39
Issue number6
DOIs
Publication statusPublished - 1 Dec 2002
Externally publishedYes

Keywords

  • Counterexamples
  • Elliptic
  • Error estimates
  • Finite volume

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics
  • Computational Mathematics

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