Discrete maximum principle for FE solutions of the diffusion-reaction problem on prismatic meshes

Authors:
Antti Hannukainen;Sergey Korotov;Tomáš Vejchodský
Affiliations:
Institute of Mathematics, Helsinki University of Technology, P.O. Box 1100, FIN-02015 Espoo, Finland;Institute of Mathematics, Helsinki University of Technology, P.O. Box 1100, FIN-02015 Espoo, Finland;Institute of Mathematics, Czech Academy of Sciences, itná 25, CZ-115 67 Prague 1, Czech Republic
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

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Abstract

In this paper we analyse the discrete maximum principle (DMP) for a stationary diffusion-reaction problem solved by means of prismatic finite elements. We derive geometric conditions on the shape parameters of the prismatic partitions which guarantee validity of the DMP. The presented numerical tests show the sharpness of the obtained conditions.