Geometrical mesh improvement properties of delaunay terminal edge refinement

Abstract

The use of edge based refinement in general, and Delaunay terminal edge refinement in particular are well established for adaptive meshing, but largely on a heuristic basis. In this paper, we present some theoretical results on geometric improvement, and it limitations, for these methods. Angle bounds for simple longest edge bisection are reviewed and extended. Terminal edges are local maximal edges in a mesh; two additional bounds that apply to simple bisection of terminal edges in Delaunay meshes are presented. The angle properties of Delaunay insertion of the midpoint of a terminal edge are described.