hp-dGFEM for Second-Order Elliptic Problems in Plyhedra I: Stability and Quasioptimality on Geometric Meshes

Schötzau, D.; Schwab, Ch.; Wihler, T. P. (2013). hp-dGFEM for Second-Order Elliptic Problems in Plyhedra I: Stability and Quasioptimality on Geometric Meshes. Siam journal on numerical analysis, 51(3), pp. 1610-1633. Society for Industrial and Applied Mathematics 10.1137/090772034

Preview	Text report13-10.pdf - Submitted Version Available under License Publisher holds Copyright. Download (681kB) | Preview
	Text __ubnetapp02_user$_brinksma_Downloads_hp-DGFEM.pdf - Published Version Restricted to registered users only Available under License Publisher holds Copyright. Download (416kB)

We introduce and analyze hp-version discontinuous Galerkin (dG) finite element
methods for the numerical approximation of linear second-order elliptic boundary-value problems in three-dimensional polyhedral domains. To resolve possible corner-, edge- and corner-edge singularities, we consider hexahedral meshes that are geometrically and anisotropically refined toward the corresponding neighborhoods. Similarly, the local polynomial degrees are increased linearly and possibly anisotropically away from singularities. We design interior penalty hp-dG methods and prove that they are well-defined for problems with singular solutions and stable under the proposed hp-refinements. We establish (abstract) error bounds that will allow us to prove exponential rates of convergence in the second part of this work.

Interest & Impact

Downloads

347 since deposited on 12 Mar 2014
27 in the past 12 months

Citations

5 Citations in Web of Science ®
6 Citations in Scopus

Search

in Google Scholar™

Services

Actions (login required)

Edit item

Actions (login required)

Edit item