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.
@article{arxiv.2404.11603,
title = {Isoparametric Virtual Element Methods},
author = {Andrea Cangiani and Andreas Dedner and Matthew Hubbard and Harry Wells},
journal= {arXiv preprint arXiv:2404.11603},
year = {2024}
}