Skip to content
Publicly Available Published by De Gruyter July 2, 2013

Some Error Estimates for the Finite Volume Element Method for a Parabolic Problem

  • Panagiotis Chatzipantelidis EMAIL logo , Raytcho Lazarov and Vidar Thomée


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.

Published Online: 2013-07-02
Published in Print: 2013-07-01

© 2013 by Walter de Gruyter Berlin Boston

Downloaded on 2.6.2023 from
Scroll to top button