[Zurück]

E. Georgoulis, E. Hall, J. Melenk:
"On the suboptimality of the $p$-version interior penalty discontinuous Galerkin method";
in: "ASC Report 03/2009", herausgegeben von: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2009, ISBN: 978-3-902627-02-5.

We address the question of the rates of convergence of the p-version interior penalty discontinuous
Galerkin method (p-IPDG) for second order elliptic problems with non-homogeneous Dirichlet boundary
conditions. It is known that the p-IPDG method admits slightly suboptimal a-priori bounds with
respect to the polynomial degree (in the Hilbertian Sobolev space setting). An example for which the
suboptimal rate of convergence with respect to the polynomial degree is both proven theoretically and
validated in practice through numerical experiments is presented. Moreover, the performance of p-
IPDG on the related problem of p-approximation of corner singularities is assessed both theoretically
and numerically, witnessing an almost doubling of the convergence rate of the p-IPDG method.

http://dx.doi.org/10.1007/s10915-009-9315-z

http://www.asc.tuwien.ac.at/preprint/2009/asc03x2009.pdf