Displaying similar documents to “Generalization of the Zlámal condition for simplicial finite elements in ℝ d ”

Nonobtuse tetrahedral partitions that refine locally towards Fichera-like corners

Larisa Beilina, Sergey Korotov, Michal Křížek (2005)

Applications of Mathematics

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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.

Colouring polytopic partitions in ℝ d

Michal Křížek (2002)

Mathematica Bohemica

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We consider face-to-face partitions of bounded polytopes into convex polytopes in ℝ d for arbitrary d ≥ 1 and examine their colourability. In particular, we prove that the chromatic number of any simplicial partition does not exceed d + 1 . Partitions of polyhedra in ℝ 3 into pentahedra and hexahedra are 5 - and 6 -colourable, respectively. We show that the above numbers are attainable, i.e., in general, they cannot be reduced.

Simplicial finite elements in higher dimensions

Jan Brandts, Sergey Korotov, Michal Křížek (2007)

Applications of Mathematics

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Over the past fifty years, finite element methods for the approximation of solutions of partial differential equations (PDEs) have become a powerful and reliable tool. Theoretically, these methods are not restricted to PDEs formulated on physical domains up to dimension three. Although at present there does not seem to be a very high practical demand for finite element methods that use higher dimensional simplicial partitions, there are some advantages in studying the methods independent...