  This work concerns adaptive refinement procedures for meshes of polygonal
virtual elements. Specifically, refinement procedures previously proposed by
the authors for structured meshes are generalized for the challenging case of
arbitrary element geometries arising in unstructured/Voronoi discretizations.
Here, structured and unstructured meshes are considered and are created via
Voronoi tessellation of sets of structured and unstructured seed points
respectively. The novel mesh refinement procedures for both structured and
unstructured meshes allow for accurate and efficient application of the virtual
element method to challenging elastic problems in two-dimensions. The results
demonstrate that the high efficacy of the proposed refinement procedures on
structured meshes, as seen in previous work by the authors, is also achieved in
the case of unstructured/Voronoi meshes. The versatility and efficacy of the
refinement procedures demonstrated over a variety of mesh types indicates that
the procedures are well-suited to virtual element applications.
