A Coarsening Algorithm on Adaptive Red-Green-Blue Refined Meshes
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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 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 without explicitly knowing the refinement history. To this end, we examine the local structure of these meshes, find an easy-to-verify criterion to coarsen red-green-blue meshes and prove that this criterion generates meshes with the desired properties. However, it does not guarantee that the set of nodes admissible for coarsening is non-empty. Therefore, we also present an additional algorithm that uses the main ideas of this criterion to always allow for local coarsening. We present a MATLAB implementation built on the red-green-blue refinement routine of the ameshref-package.
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