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.

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