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The discrete maximum principle for linear simplicial finite element approximations of a reaction–diffusion problem

✍ Scribed by Jan H. Brandts; Sergey Korotov; Michal Křížek

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
761 KB
Volume
429
Category
Article
ISSN
0024-3795

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✦ Synopsis

This paper provides a sufficient condition for the discrete maximum principle for a fully discrete linear simplicial finite element discretization of a reaction-diffusion problem to hold. It explicitly bounds the dihedral angles and heights of simplices in the finite element partition in terms of the magnitude of the reaction coefficient and the spatial dimension. As a result, it can be computed how small the acute simplices should be for the discrete maximum principle to be valid. Numerical experiments suggest that the bound, which considerably improves a similar bound in [P.G. Ciarlet, P.-A. Raviart, Maximum principle and uniform convergence for the finite element method, Comput. Methods Appl. Mech. Eng. 2 (1973) 17-31], is in fact sharp.

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