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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:

@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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