In this paper we initiate the investigation of Virtual Elements with curved faces. We consider the case of a fixed curved boundary in two dimensions, as it happens in the approximation of problems posed on a curved domain or with a curved interface. While an approximation of the domain with polygons leads, for degree of accuracy k≥2, to a sub-optimal rate of convergence, we show (both theoretically and numerically) that the proposed curved VEM lead to an optimal rate of convergence.
@article{arxiv.1711.04306,
title = {The Virtual Element Method with curved edges},
author = {L. Beirão da Veiga and A. Russo and G. Vacca},
journal= {arXiv preprint arXiv:1711.04306},
year = {2018}
}