Quasi-optimal mesh generation for the virtual element method: A fully adaptive remeshing procedure - van Huyssteen, Daniel; Rivarola, Felipe Lopez; Etse, Guillermo; Steinmann, Paul (Computer Methods in Applied Mechanics and Engineering, 2025)
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.
CRIS-Team Scopus Importer:2025-02-17
Keywords: Adaptivity; Coarsening; Hierarchy-free; Quasi-optimal mesh; Refinement; Virtual element method