Institute for Computational Mathematics
Joint Research Institute for Applied Mathematics

Maximum-Principles in
Parabolic Finite Element Problems


Prof. Vidar Thomée

Department of Mathematical Sciences
Chalmers University of Technology
Gothenburg, Sweden


Tuesday, 2 February 2010
11:30am -12:30pm (Preceded by Tea Reception at 11:00am)
OEE601-603, Oen Hall Building (East Wing),
Ho Sin Hang Campus, Hong Kong Baptist University

We consider piecewise linear finite element discretizations of the model initial-boundary value problem for the homogeneous heat equation, and discuss the validity of the associated discrete maximum-principles. We demonstrate that for the spatially semidiscrete standard Galerkin approximation, the maximum-principle is not valid in general. However, as was shown by Fujii in 1973, the maximum-principle holds for the lumped mass modification, when the triangulation is of Delaunay type, and this condition on the triangulation is essentially sharp. We also present some results for the simplest time stepping analogues of these approximations.

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