Some error estimates for the finite volume element method for a parabolic problem

Panagiotis Chatzipantelidis, Raytcho Lazarov, Vidar Thomée

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

We study spatially semidiscrete and fully discrete finite volume element methods for the homogeneous heat equation with homogeneous Dirichlet boundary conditions and derive error estimates for smooth and nonsmooth initial data. We show that the results of our earlier work [Math. Comp. 81 (2012), 1-20] for the lumped mass method carry over to the present situation. In particular, in order for error estimates for initial data only in L2 to be of optimal second order for positive time, a special condition is required, which is satisfied for symmetric triangulations. Without any such condition, only first order convergence can be shown, which is illustrated by a counterexample. Improvements hold for triangulations that are almost symmetric and piecewise almost symmetric. © 2013 Institute of Mathematics.
Original languageEnglish (US)
Pages (from-to)251-279
Number of pages29
JournalComputational Methods in Applied Mathematics
Volume13
Issue number3
DOIs
StatePublished - Jul 1 2013
Externally publishedYes

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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