A Coarsening Algorithm on Adaptive Red-Green-Blue Refined Meshes

Abstract: Adaptive meshing is a fundamental component of adaptive finite element methods. This includes refining and coarsening meshes locally. In this work, we are concerned with the red-green-blue refinement strategy in two dimensions and its counterpart - coarsening. In general, coarsening algorithms are mostly based on an explicitly given refinement history. In this work, we present a coarsening algorithm on adaptive red-green-blue meshes in two dimensions without explicitly knowing the refinement history. To this end, we examine the local structure of these meshes, find an easy-to-verify criterion to adaptively coarsen red-green-blue meshes and prove that this criterion generates meshes with the desired properties. We present a MATLAB implementation built on the red-green-blue refinement routine of the ameshref-package.