# hp-dGFEM for Second-Order Elliptic Problems in Plyhedra II: Exponential Convergence

Schötzau, D.; Schwab, Ch.; Wihler, T. P. (2013). hp-dGFEM for Second-Order Elliptic Problems in Plyhedra II: Exponential Convergence. Siam journal on numerical analysis, 51(4), pp. 2005-2035. Society for Industrial and Applied Mathematics 10.1137/090774276

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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 homogeneous Dirichlet boundary conditions and piecewise analytic data in three-dimensional polyhedral domains. More precisely, we shall analyze the convergence of the $hp$-IP dG methods considered in [D. Schötzau, C. Schwab, T. P. Wihler, SIAM J. Numer. Anal., 51 (2013), pp. 1610--1633] based on axiparallel $\sigma$-geometric anisotropic meshes and $\bm{s}$-linear anisotropic polynomial degree distributions.

#### Item Type:

Journal Article (Original Article)

#### Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

Wihler, Thomas

#### Subjects:

500 Science > 510 Mathematics

1095-7170

#### Publisher:

Society for Industrial and Applied Mathematics

English

Mario Amrein

#### Date Deposited:

12 Mar 2014 11:32

#### Last Modified:

06 Aug 2019 14:04

#### Publisher DOI:

10.1137/090774276

#### BORIS DOI:

10.7892/boris.41961

#### URI:

https://boris.unibe.ch/id/eprint/41961

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