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

Zhu, L. and Giani, S. and Houston, P. and Schötzau, D. (2011) '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., 21 (02). pp. 267-306.

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 error 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
Keywords:Discontinuous Galerkin methods, a posteriori error estimation, hp-adaptivity, Elliptic problems.
Full text:(AM) Accepted Manuscript
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Status:Peer-reviewed
Publisher Web site:http://dx.doi.org/10.1142/S0218202511005052
Publisher statement:Electronic version of an article published as Mathematical Models and Methods in Applied Sciences, 21, 02, 2011, 267-306, doi: 10.1142/S0218202511005052 © copyright World Scientific Publishing Company http://www.worldscientific.com/worldscinet/m3as
Date accepted:No date available
Date deposited:20 April 2015
Date of first online publication:February 2011
Date first made open access:No date available

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