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.

翻译：在自适应重网格的背景下，虚拟单元法相较于有限元法具有显著优势。虚拟单元法的吸引人特性，例如允许任意单元几何形状和无缝支持'悬挂'节点，已催生了许多关于误差估计和自适应性的研究。然而，这些研究主要聚焦于自适应细化技术，而对开发完全自适应重网格程序所需的自适应粗化（即逆细化）技术关注甚少。本文提出用于识别待粗化单元块/簇的新型指示器，以及一种执行粗化的创新流程。这些指示器在潜在单元块而非单个单元上进行计算，以识别最适合粗化的单元组合。该粗化流程具有鲁棒性，适用于结构化网格和非结构化/沃罗诺伊单元网格。数值结果表明，所提出的粗化程序具有高度有效性，且在粗化过程中网格演变合理。实验证明，关键网格几何特征（如非凸角点和孔洞）在粗化过程中得以保留，并且网格在工程师关注的区域（如奇点附近）保持精细。