A unifying theory of a posteriori error control for discontinuous Galerkin FEM

Carstensen, Carsten, Gudi, Thirupathi and Jensen, Max (2009) A unifying theory of a posteriori error control for discontinuous Galerkin FEM. Numerische Mathematik, 112 (3). pp. 363-379. ISSN 0029-599X

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Abstract

A unified a posteriori error analysis is derived in extension of Carstensen (Numer Math 100:617–637, 2005) and Carstensen and Hu (J Numer Math 107(3):473–502, 2007) for a wide range of discontinuous Galerkin (dG) finite element methods (FEM), applied to the Laplace, Stokes, and Lamé equations. Two abstract assumptions (A1) and (A2) guarantee the reliability of explicit residual-based computable error estimators. The edge jumps are recast via lifting operators to make arguments already established for nonconforming finite element methods available. The resulting reliable error estimate is applied to 16 representative dG FEMs from the literature. The estimate recovers known results as well as provides new bounds to a number of schemes.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QA Mathematics > QA0297 Numerical analysis
Depositing User: Max Jensen
Date Deposited: 19 Jun 2013 10:42
Last Modified: 19 Jun 2013 10:42
URI: http://sro.sussex.ac.uk/id/eprint/45502
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