Similarity classes generated by the 8T-LE partition applied to trirectangular tetrahedra

Abstract

When the 8T-LE partition is recursively applied to any initial trirectangular tetrahedron T, only a finite number of dissimilar tetrahedra are generated. It implies the stability of the meshes. At each step of refinement the number of right-type or path tetrahedra grows, so the quality of the obtained meshes improves. The minimum angle condition and the maximum angle condition are trivially satisfied, since the number of similarity classes is finite.