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Tetrahedral grid refinement. (English) Zbl 0839.65135
Adaptive techniques in the finite element methods optimize the number of unknowns by fitting the corresponding discretization. In three-dimensional problems, the underlying discretization mesh is given by a triangulation with the help of tetrahedral grids. Thus, the author considers an adaptive method to generate sequences of triangulations which are consistent (roughly spoken, this is the prevention of so-called “hanging nodes”) and stable (the interior angles of all elements are uniformly bounded away from zero).
To make compatible adaptivity, consistency, and stability the refinement algorithm is constructed in three steps. First, a basic strategy is defined for the subdivision of a tetrahedron into eight subtetrahedra of equal volume (a regular strategy). Second, irregular refinement rules are chosen for elements not refined regularly but sharing a refined edge or side of another element. Finally, a global refinement algorithm describes how the local rules can be combined. A routine and subroutines of the whole algorithm are formulated independently of any programming language – a useful tool to understand the construction in all details.

65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
Full Text: DOI
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