On Preservation of Positivity in Some Finite Element Methods for the Heat Equation
Artikel i vetenskaplig tidskrift, 2015

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.

Lumped Mass

Spatially Semidiscrete

Finite Volume Element Method

Finite Element Method

Positivity Preserving

Heat Equation

Fully Discrete

Finite Element Discretization


P Chatzipantelidis

Panepistimio Kritis

Z. Horvath

Szechenyi Istvan Egyetem

Vidar Thomee

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Matematik

Computational Methods in Applied Mathematics

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

Vol. 15 417-437