Isoparametric Virtual Element Methods
<|reference_start|>Isoparametric Virtual Element Methods: We present two approaches to constructing isoparametric Virtual Element Methods of arbitrary order for linear elliptic partial differential equations on general two-dimensional domains. The first method approximates the variational problem transformed onto a computational reference domain. The second method computes a virtual domain and uses bespoke polynomial approximation operators to construct a computable method. Both methods are shown to converge optimally, a behaviour confirmed in practice for the solution of problems posed on curved domains.<|reference_end|>
@article{cangiani2024isoparametric,
    title={Isoparametric Virtual Element Methods},
    author={Andrea Cangiani, Andreas Dedner, Matthew Hubbard, Harry Wells},
    journal={arXiv preprint arXiv:2404.11603},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.11603},
    primaryClass={math.NA cs.NA}
}