Convergence speed of generalized longest-edge-based refinement

Abstract

In the refinement of meshes, one wishes to iteratively subdivide a domain following geometrical partition rules. The aim is to obtain a new discretized domain with adapted regions. We prove that the Longest Edge n -section of triangles for n⩾4 produces a finite sequence of triangle meshes with guaranteed convergence of diameters and review previous result when n equals 2 and 3. We give upper and lower bounds for the convergence speed in terms of diameter reduction. Then we fill the gap in the analysis of the diameters convergence for generalized Longest Edge based refinement. In addition, we give a numerical study for the case of n=4 , the so-called LE quatersection, evidencing its utility in adaptive mesh refinement.