On the suboptimality of the p-version interior penalty discontinuous Galerkin method
Georgoulis, Emmanuil H. and Hall, Edward and Melenk, Jens Markus (2009) On the suboptimality of the p-version interior penalty discontinuous Galerkin method. Journal of Scientific Computing . ISSN 0885-7474 (In Press)
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.
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