Quasi-optimal mesh generation for the virtual element method: A fully adaptive remeshing procedure

The mesh flexibility offered by the virtual element method has made it increasingly popular 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 notion 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 non-hierarchical remeshing procedure for the virtual element method is presented for two-dimensional elastic problems. 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. Numerical results additionally demonstrate the suitability of the fully adaptive procedure for dynamic problems. • A first-order virtual element method is presented for linear elasticity. • A novel fully adaptive remeshing procedure for polygonal meshes is proposed. • The procedure is suitable for error targets and computational load targets. • The procedure generates quasi-optimal meshes with quasi-even error distribution. • The procedure is suitable for static and dynamic/transient problems.