APPLICATIONS OF MATHEMATICS, Vol. 50, No. 6, pp. 569-581, 2005

Nonobtuse tetrahedral partitions that
refine locally towards Fichera-like corners

Larisa Beilina, Sergey Korotov, Michal Krizek

L. Beilina, Department of Mathematics, University of Basel, Rheinsprung 21, CH-4051 Basel, Switzerland, e-mail:; S. Korotov, Helsinki University of Technology, Institute of Mathematics, P.O. Box 1100, FI-02015 Espoo, Finland, e-mail:; Michal Krizek, Mathematical Institute of the Academy of Sciences of the Czech Republic, Zitna 25, CZ-115 67 Praha 1, Czech Republic, e-mail:

Abstract: Linear tetrahedral finite elements whose dihedral angles are all nonobtuse guarantee the validity of the discrete maximum principle for a wide class of second order elliptic and parabolic problems. In this paper we present an algorithm which generates nonobtuse face-to-face tetrahedral partitions that refine locally towards a given Fichera-like corner of a particular polyhedral domain.

Keywords: partial differential equations, finite element method, path tetrahedron, linear tetrahedral finite element, discrete maximum principle, reentrant corner, Fichera vertex, nonlinear heat conduction

Classification (MSC 2000): 65N30, 65N50, 51M20

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