Uniform Refinement of a Tetrahedron

A uniform refinement strategy for a tetrahedron is presented. Most finite element theories are based on the assumption that the tetrahedral elements in the refinement do not degenerate. In this paper, the author presents a refinement strategy that is nondegenerate and uniform for the model tetrahedra considered and quasi uniform for arbitrary tetrahedra. It can be used to construct nested, multilevel triangulations. At level j of refinement, an arbitrary nondegenerate tetrahedron in the initial triangulation is partitioned into $2^{3j} $ tetrahedra of equal volume. This refinement strategy can be implemented easily by partitioning block elements instead of the more complicated tetrahedral elements. This feature makes the use of tetrahedral elements attractive in a computer code.