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Adaptive meshing includes local refinement as well as coarsening of meshes.Typically, coarsening algorithms are based on an explicit refinement history.In this work, we deal with local coarsening algorithms that build on therefinement strategies for triangular and quadrilateral meshes implemented inthe ameshref package (Funken and Schmidt 2018, 2019). The ameshref package is aMATLAB-toolbox for research and teaching purposes which offers the user acertain flexibility in the REFINE step of an adaptive finite element method butcan also be used in other contexts like computer graphics. This toolbox is nowbe extended by the coarsening option. In ameshref, no explicit informationabout the refinement process is stored, but is instead implicit in the datastructure. In this work, we present coarsening algorithms that useeasy-to-verify criteria to coarsen adaptively generated meshes by exploitingthe data structure. Thereby, the desired properties are guaranteed andcomputational efficiency is maintained. A MATLAB implementation and somenumerical examples are discussed in this work and are included in full in thetoolbox ameshcoars (Funken and Schmidt 2020).

Local Coarsening Algorithms on Adaptively Refined Meshes in 2D and Their Efficient Implementation in MATLAB