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.

翻译：本文关注多边形虚拟单元网格的自适应细化方法。具体而言，将作者先前针对结构化网格提出的细化算法推广至非结构化/ Voronoi离散化中任意单元几何形状这一具有挑战性的情形。本文分别考虑结构化与非结构化网格，它们通过对结构化与随机种子点集进行Voronoi剖分生成。针对两类网格提出的新型细化方法使得虚拟单元方法能够精确高效地应用于二维弹性问题。结果表明：作者前期工作中证实的结构化网格细化方案的高效性，在非结构化/ Voronoi网格中同样得以实现。该细化方法在多种网格类型中展现出的普适性与高效性，表明其完全适用于虚拟单元应用场景。