The mesh flexibility offered by the virtual element method through the permission of arbitrary element geometries, and the seamless incorporation of `hanging' nodes, has made the method increasingly attractive in the context of adaptive remeshing. There exists a healthy literature concerning error estimation and adaptive refinement techniques for virtual elements while the topic of adaptive coarsening (i.e. de-refinement) is in its infancy. The creation of a quasi-optimal mesh is based on the principle of quasi-even error distribution over the elements which inherently relies on localized refinement and coarsening techniques. Thus, necessitating a fully adaptive remeshing procedure. In this work a novel fully adaptive remeshing procedure for the virtual element method is presented. Additionally, novel procedures are proposed for the identification of elements qualifying for refinement or coarsening based on user-defined targets. Specifically, a target percentage error, target number of elements, or target number of nodes can be selected. Numerical results demonstrate that the adaptive remeshing procedure can meet any prescribed target while creating a quasi-optimal mesh. The proposed fully adaptive procedure is of particular interest in engineering applications requiring an efficient simulation of a given accuracy, or desiring a simulation with the maximum possible accuracy for a given computational constraint.

翻译：虚拟单元法通过允许任意单元几何形状以及无缝整合"悬挂"节点所提供的网格灵活性，使其在自适应重网格化背景下日益受到关注。目前已有大量关于虚拟单元法误差估计与自适应细化技术的文献，而自适应粗化（即逆细化）研究尚处于起步阶段。准最优网格的创建基于单元间准均匀误差分布原则，这本质上依赖于局部细化与粗化技术，因此需要完全自适应的重网格化流程。本研究提出了一种适用于虚拟单元法的新型完全自适应重网格化流程，并创新性地建立了基于用户设定目标的单元细化/粗化判定机制：可选择设定目标误差百分比、目标单元数量或目标节点数量。数值结果表明，该自适应重网格化流程能在创建准最优网格的同时满足任意预设目标。所提出的完全自适应流程对于以下工程应用具有特殊价值：需要以给定精度进行高效仿真，或期望在特定计算约束下实现最大可能精度的仿真场景。