Some error estimates for the finite volume element method for a parabolic problem
Journal article, 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.

Finite Volume Method

Error Estimates

Nonsmooth Initial Data

Parabolic Partial Differential Equations

Author

P Chatzipantelidis

University of Crete

R. D. Lazarov

Bulgarian Academy of Sciences

Texas A&M University

Vidar Thomee

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

Computational Methods in Applied Mathematics

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

Vol. 13 3 251-279

Subject Categories

Computational Mathematics

Roots

Basic sciences

DOI

10.1515/cmam-2012-0006

More information

Latest update

7/8/2021 1