Refinement strategies related to cubic tetrahedral meshes. (English) Zbl 1422.65433

Petrov, Miroslav S.; Todorov, Todor D.

Appl. Numer. Math. 137, 169-183 (2019).

This paper is concerned about the mesh refinement techniques for application of finite element multigrid methds with cubic basis functions. The popular 27-refinement strategy is analyzed with respect to the number of congruence classes and measure of degeneracy. This strategy is nonsymmetric and dependent on the numbering of the nodes. A new canonical refinement strategy (CRS) is proposed. Compared to the 27-refinement strategy, the CRS reduces the number of congruence classes, the measure of degeneracy and overall computational cost. The advantages of the CRS are demonstrated by solving a strongly anisotropic diffusion problem.

Reviewer: Jichun Li (Las Vegas)

MSC:

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

Keywords:

measure of degeneracy; congruence classes; refinement strategies

Software:

LBIE

References:

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