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

• DOI: 10.1515/cmam-2015-0018
• Publication Date: 2015-08-04T12:20:25Z
• Authors: Panagiotis Chatzi...; Zoltan Horváth; Vidar Thomée
• Keywords: Heat equation

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