Some error estimates for the finite volume element method for a parabolic problem
Artikel i vetenskaplig tidskrift, 2013

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), no. 277, 1–20; MR2833485 (2012f:65159)] 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.

Parabolic Partial Differential Equations

Finite Volume Method

Error Estimates

Nonsmooth Initial Data


P Chatzipantelidis

Panepistimio Kritis

R. D. Lazarov

Texas A and M University

Institute of Mathematics and Informatics Bulgarian Academy of Sciences

Vidar Thomee

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Matematik

Computational Methods in Applied Mathematics

1609-4840 (ISSN) 1609-9389 (eISSN)

Vol. 13 251-279




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