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.
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 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.
© 2015 by De Gruyter