Non-conforming harmonic virtual element method: $h$- and $p$-versions
Abstract
We study the - and -versions of non-conforming harmonic virtual element methods (VEM) for the approximation of the Dirichlet-Laplace problem on a 2D polygonal domain, providing quasi-optimal error bounds. Harmonic VEM do not make use of internal degrees of freedom. This leads to a faster convergence, in terms of the number of degrees of freedom, as compared to standard VEM. Importantly, the technical tools used in our -analysis can be employed as well in the analysis of more general non-conforming finite element methods and VEM. The theoretical results are validated in a series of numerical experiments. The -version of the method is numerically tested, demonstrating exponential convergence with rate given by the square root of the number of degrees of freedom.
Cite
@article{arxiv.1801.00578,
title = {Non-conforming harmonic virtual element method: $h$- and $p$-versions},
author = {Lorenzo Mascotto and Ilaria Perugia and Alexander Pichler},
journal= {arXiv preprint arXiv:1801.00578},
year = {2018}
}