Contributions to Books:

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

English abstract:
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.

"Official" electronic version of the publication (accessed through its Digital Object Identifier - DOI)

Electronic version of the publication:

Created from the Publication Database of the Vienna University of Technology.