On a Bisection Algorithm That Produces Conforming Locally Refined Simplicial Meshes

Abstract

Antti Hannukainen, Sergey Korotov, Michal Křížek: On a bisection algorithm that produces conforming locally refined simplicial meshes; Helsinki University of Technology Institute of Mathematics Research Reports A567 (2009).Abstract: First we introduce a mesh density function that serves as a criterion to decide, where a simplicial mesh should be fine (dense) and where it should be coarse. Further, we propose a new bisection algorithm that chooses for bisection an edge in a given mesh associated with the maximum value of the mesh density function. Dividing this edge at its midpoint, we correspondingly bisect all simplices sharing this edge. Repeating this process, we construct a family of conforming nested simplicial meshes. We prove that the corresponding mesh size tends to zero for d = 2, 3. AMS subject classifications: 65N50, 65M50Keywords: bisection algorithm, simplicial elements, conforming finite element method, local refinements, nested meshes