On Preservation of Positivity in Some Finite Element Methods for the Heat Equation
Journal article, 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.
Spatially Semidiscrete
Finite Element Discretization
Positivity Preserving
Finite Volume Element Method
Lumped Mass
Fully Discrete
Finite Element Method
Heat Equation
Author
P Chatzipantelidis
University of Crete
Z. Horvath
Szechenyi Istvan Egyetem
Vidar Thomee
Chalmers, Mathematical Sciences, Mathematics
University of Gothenburg
Computational Methods in Applied Mathematics
1609-4840 (ISSN) 1609-9389 (eISSN)
Vol. 15 4 417-437Subject Categories (SSIF 2011)
Computational Mathematics
DOI
10.1515/cmam-2015-0018