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

TL;DR

This paper introduces a fully adaptive remeshing procedure for the virtual element method that achieves quasi-optimal meshes by balancing error distribution through localized refinement and coarsening, tailored to user-defined targets.

Contribution

It presents a novel fully adaptive remeshing algorithm for virtual elements, including new methods for element refinement and coarsening based on user targets.

Findings

The method can meet prescribed error or element targets.

It produces quasi-optimal meshes with balanced error distribution.

Applicable to engineering problems requiring efficient, accurate simulations.

Abstract

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.