Quasi-optimal mesh generation for the virtual element method: A fully adaptive remeshing procedure
<|reference_start|>Quasi-optimal mesh generation for the virtual element method: A fully adaptive remeshing procedure: 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.<|reference_end|>
@article{van huyssteen2024quasi-optimal,
    title={Quasi-optimal mesh generation for the virtual element method: A fully
  adaptive remeshing procedure},
    author={Daniel van Huyssteen, Felipe Lopez Rivarola, Guillermo Etse, Paul
  Steinmann},
    journal={arXiv preprint arXiv:2407.13665},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.13665},
    primaryClass={math.NA cs.NA}
}