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Weakened acute type condition for tetrahedral triangulations and the discrete maximum principle

Authors: Sergey Korotov, Michal Krízek and Pekka Neittaanmäki
Journal: Math. Comp. 70 (2001), 107-119
MSC (2000): Primary 65N30
Published electronically: May 23, 2000
MathSciNet review: 1803125
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Abstract: We prove that a discrete maximum principle holds for continuous piecewise linear finite element approximations for the Poisson equation with the Dirichlet boundary condition also under a condition of the existence of some obtuse internal angles between faces of terahedra of triangulations of a given space domain. This result represents a weakened form of the acute type condition for the three-dimensional case.

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Additional Information

Sergey Korotov
Affiliation: University of Jyväskylä, Department of Mathematical Information Technology, P.O. Box 35, FIN–40351 Jyväskylä, Finland

Michal Krízek
Affiliation: Mathematical Institute, Academy of Sciences, Žitná 25, CZ–11567 Prague 1, Czech Republic

Pekka Neittaanmäki
Affiliation: University of Jyväskylä, Department of Mathematical Information Technology, P.O. Box 35, FIN–40351 Jyväskylä, Finland

Keywords: Maximum principle, Poisson equation, weakened acute type condition, linear tetrahedral finite element
Received by editor(s): January 26, 1999
Published electronically: May 23, 2000
Additional Notes: The first author was partly supported by the Academy of Finland, Grant no. 752205, and partly by the Mittag-Leffler Institute, Djursholm, Sweden
The second author was supported by the Grant no. 201/98/0528 of the Grant Agency of Czech Republic
Article copyright: © Copyright 2000 American Mathematical Society

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