On numerical regularity of trisection-based algorithms in 3D

Abstract

The longest-edge (LE-) trisection of the given tetrahedron is obtained by joining two equally spaced points on its longest edge with the opposite vertices, and, thus, splitting the tetrahedron into three sub-tetrahedra. On the base such LE-trisections we introduce and numerically test the refinement algorithms for tetrahedral meshes. Computations conducted show that the quality of meshes generated by these algorithms does not seem to degenerate.