Refinement based on longest-edge and self-similar four-triangle partitions

Abstract

The triangle longest-edge bisection constitutes an efficient scheme for refining a mesh by reducing the obtuse triangles, since the largest interior angles are subdivided. One of these schemes is the four-triangle longest-edge (4T-LE) partition. Moreover, the four triangle self-similar (4T-SS) partition of an acute triangle yields four sub-triangles similar to the original one. In this paper we present a hybrid scheme combining the 4T-LE and the 4T-SS partitions which use the longest-edge based refinement. Numerical experiments illustrate improvement in angles and quality. The benefits of the algorithm suggest its use as an efficient tool for mesh refinement in the context of Finite Element computations.