  In the context of adaptive remeshing, the virtual element method provides
significant advantages over the finite element method. The attractive features
of the virtual element method, such as the permission of arbitrary element
geometries, and the seamless permission of 'hanging' nodes, have inspired many
works concerning error estimation and adaptivity. However, these works have
primarily focused on adaptive refinement techniques with little attention paid
to adaptive coarsening (i.e. de-refinement) techniques that are required for
the development of fully adaptive remeshing procedures. In this work novel
indicators are proposed for the identification of patches/clusters of elements
to be coarsened, along with a novel procedure to perform the coarsening. The
indicators are computed over prospective patches of elements rather than on
individual elements to identify the most suitable combinations of elements to
coarsen. The coarsening procedure is robust and suitable for meshes of
structured and unstructured/Voronoi elements. Numerical results demonstrate the
high degree of efficacy of the proposed coarsening procedures and sensible mesh
evolution during the coarsening process. It is demonstrated that critical mesh
geometries, such as non-convex corners and holes, are preserved during
coarsening, and that meshes remain fine in regions of interest to engineers,
such as near singularities.
