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.
Mascotto, L., Perugia, I., Pichler, A. (2018). Non-conforming Harmonic Virtual Element Method: h - and p -Versions. JOURNAL OF SCIENTIFIC COMPUTING, 77(3), 1874-1908 [10.1007/s10915-018-0797-4].
Non-conforming Harmonic Virtual Element Method: h - and p -Versions
Mascotto L.;
2018
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.