Longest-edge algorithms for size-optimal refinement of triangulations

Abstract

Longest-edge refinement algorithms were designed to iteratively refine the mesh for finite-element applications by maintaining mesh quality (assuring a bound on the smallest angle). In this paper we improve geometrical results on longest-edge refinement algorithms and provide precise bounds on the refinement propagation. We prove that the iterative application of the algorithm gradually reduces the average extent of the propagation per target triangle, tending to affect only two triangles. We also include empirical results which are in complete agreement with the theory.