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arXiv · 1801.00578

Non-conforming harmonic virtual element method: $h$- and $p$-versions

Lorenzo Mascotto·Ilaria Perugia·Alexander Pichler
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Abstract

We study the $h$- and $p$-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 $p$-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 $hp$-version of the method is numerically tested, demonstrating exponential convergence with rate given by the square root of the number of degrees of freedom.

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Lorenzo Mascotto, Ilaria Perugia, Alexander Pichler. 2018-01-02. Non-conforming harmonic virtual element method: $h$- and $p$-versions. https://arxiv.org/abs/1801.00578

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