  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 the
refinement strategies for triangular and quadrilateral meshes implemented in
the ameshref package (Funken and Schmidt 2018, 2019). The ameshref package is a
MATLAB-toolbox for research and teaching purposes which offers the user a
certain flexibility in the REFINE step of an adaptive finite element method but
can also be used in other contexts like computer graphics. This toolbox is now
be extended by the coarsening option. In ameshref, no explicit information
about the refinement process is stored, but is instead implicit in the data
structure. In this work, we present coarsening algorithms that use
easy-to-verify criteria to coarsen adaptively generated meshes by exploiting
the data structure. Thereby, the desired properties are guaranteed and
computational efficiency is maintained. A MATLAB implementation and some
numerical examples are discussed in this work and are included in full in the
toolbox ameshcoars (Funken and Schmidt 2020).
