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Licensed Unlicensed Requires Authentication Published by De Gruyter August 4, 2015

On Preservation of Positivity in Some Finite Element Methods for the Heat Equation

Panagiotis Chatzipantelidis EMAIL logo , Zoltan Horváth and Vidar Thomée

Abstract

We consider the initial boundary value problem for the homogeneous heat equation, with homogeneous Dirichlet boundary conditions. By the maximum principle the solution is nonnegative for positive time if the initial data are nonnegative. We complement in a number of ways earlier studies of the possible extension of this fact to spatially semidiscrete and fully discrete piecewise linear finite element discretizations, based on the standard Galerkin method, the lumped mass method, and the finite volume element method. We also provide numerical examples that illustrate our findings.

MSC: 65M12; 65M60

Funding source: University of Crete Research Committee

Award Identifier / Grant number: KA 4179

Funding source: European Social Fund and the government of Hungary

Award Identifier / Grant number: TÁMOP-4.2.2.A-11/1/KONV-2012-0012


Correction Statement

Correction added after online publication 10 September 2015: Due to an error in the computer code used to compute the results in Example 2 a few changes in Sections 1 and 5.2 and Table 3 were made.


Received: 2015-2-11
Revised: 2015-6-21
Accepted: 2015-6-29
Published Online: 2015-8-4
Published in Print: 2015-10-1

© 2015 by De Gruyter

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