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

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.


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


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