On mesh coarsening procedures for the virtual element method

Abstract: 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.