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hp-dGFEM for second-order elliptic problems in polyhedra. II: Exponential convergence
by D. Schötzau and Ch. Schwab and T. Wihler
(Report number 2009-29)
Abstract
The goal of this paper is to establish exponential convergence of hp-version interior penalty (IP) discontinuous Galerkin (dG) finite element methods for the numerical approximation of linear second-order elliptic boundary-value problems with piecewise analytic data in three-dimensional polyhedral domains. More precisely, we shall analyze the convergence of the hp-IP dG methods considered in~\cite{SSW_I} which are based on $\sigma$-geometric anisotropic meshes of mapped hexahedra with $\kappa$-uniform element mappings and anisotropic polynomial degree distributions of $\mu$-bounded variation.
Keywords:
BibTeX@Techreport{SSW09_410, author = {D. Sch\"otzau and Ch. Schwab and T. Wihler}, title = {hp-dGFEM for second-order elliptic problems in polyhedra. II: Exponential convergence}, institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich}, number = {2009-29}, address = {Switzerland}, url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2009/2009-29.pdf }, year = {2009} }
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