Energy norm a-posteriori error estimation for hp-adaptive discontinuous Galerkin methods for elliptic problems in three dimensions

Zhu, Liang and Giani, Stefano and Houston, Paul and Schoetzau, Dominik (2009) Energy norm a-posteriori error estimation for hp-adaptive discontinuous Galerkin methods for elliptic problems in three dimensions. Mathematical Models and Methods in Applied Sciences (M3AS) . ISSN 0218-2025 (Submitted)

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Abstract

We develop the energy norm a-posteriori error estimation for hp-version discontinuous Galerkin (DG) discretizations of elliptic boundary-value problems on 1-irregularly, isotropically refined affine hexahedral meshes in three dimensions. We derive a reliable and efficient indicator for the errors measured in terms of the natural energy norm. The ratio of the efficiency and reliability constants is independent of the local mesh sizes and weakly depending on the polynomial degrees. In our analysis we make use of an hp-version averaging operator in three dimensions, which we explicitly construct and analyze. We use our error indicator in an hp-adaptive refinement algorithm and illustrate its practical performance in a series of numerical examples. Our numerical results indicate that exponential rates of convergence are achieved for problems with smooth solutions, as well as for problems with isotropic corner singularities.

Item Type:Article
Additional Information:Preprint of an article submitted for consideration in Mathematical Models and Methods in Applied Sciences (M3AS) ©, 2009 [copyright World Scientific Publishing Company]http://www.worldscinet.com/m3as/m3as.shtml
Schools/Departments:Faculty of Science > School of Mathematical Sciences
ID Code:1140
Deposited By:Houston, Paul
Deposited On:02 Oct 2009 09:33
Last Modified:23 Jun 2011 07:54

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