Refinement strategies related to cubic tetrahedral meshes (Q1728339)

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.