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：本研究涉及适应性网格深度学习程序的多边形虚拟元素。具体来说，前段时间作者们在结构网格上提出的细化程序，现在被推广应用到无结构/ Voronoi 离散化中出现的任意元素几何体上。在这里，我们考虑了结构网格和无结构网格，它们通过对有序和无序的种子点进行 Voronoi 分割而产生。新颖的有关结构和无结构网格的网格细化程序允许在二维挑战性弹性问题中准确和高效地应用虚拟元素方法。结果表明，作者之前在结构网格上提出的细化程序的高效性在无结构/ Voronoi 网格上也可以实现。在多种网格类型上证明了细化程序的多才多艺和高效性，表明该程序非常适合虚拟元素应用。