2018/01/02 by Mascotto, Lorenzo, Perugia, Ilaria, Pichler, Alexander
#31A05 #35J05 #65N12 #65N15 #65N30 #FOS: Mathematics #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.1801.00578
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.