**
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: ` beilina@math.unibas.ch`; * S. Korotov*, Helsinki University of Technology, Institute of Mathematics, P.O. Box 1100, FI-02015 Espoo, Finland, e-mail: ` sergey.korotov@hut.fi`; * Michal Krizek*, Mathematical Institute of the Academy of Sciences of the Czech Republic, Zitna 25, CZ-115 67 Praha 1, Czech Republic, e-mail: ` krizek@math.cas.cz`

**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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