In this work we report some results, obtained within the framework of the ERC Project CHANGE, on the impact on the performance of the virtual element method of the shape of the polygonal elements of the underlying mesh. More in detail, after reviewing the state of the art, we present a) an experimental analysis of the convergence of the VEM under condition violating the standard shape regularity assumptions, b) an analysis of the correlation between some mesh quality metrics and a set of different performance indexes, and c) a suitably designed mesh quality indicator, aimed at predicting the quality of the performance of the VEM on a given mesh.

翻译：在这项工作中,我们报告了在ERC项目变迁框架内获得的关于基本网格多边形元件形状的虚拟要素方法对性能的影响的一些结果,更详细地说,在审查了最新情况之后,我们提出:(a) 对VEM在违反标准形状正常性假设的条件下的趋同情况进行实验性分析;(b) 分析某些网格质量指标与一套不同的性能指数之间的相互关系;(c) 设计得当的网格质量指标,旨在预测VEM在特定网格上的性能质量。