hp-DGFEM FOR SECOND ORDER ELLIPTIC PROBLEMS IN POLYHEDRA II: EXPONENTIAL CONVERGENCE

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 a...

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Bibliographic Details
Published in:SIAM journal on numerical analysis 2013-01, Vol.51 (4), p.2005-2035
Main Authors: SCHÖTZAU, D., SCHWAB, Ch, WIHLER, T. P.
Format: Article
Language:English
Subjects:
Analytics
Anisotropy
Approximation
Convergence
Degrees of polynomials
Dirichlet problem
Error bounds
Galerkin methods
Interpolation
Mathematical analysis
Mathematical problems
Mathematical vectors
Polyhedra
Polyhedrons
Polynomials
Three dimensional
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Summary: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 σ-geometric anisotropic meshes and s-linear anisotropic polynomial degree distributions.
ISSN:0036-1429
1095-7170
DOI:10.1137/090774276