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An A Posteriori Error Indicator for Discontinuous Galerkin Approximations of Fourth Order Elliptic Problems

Georgoulis, Emmanuil H.; Houston, Paul; Virtanen, Juha

Authors

Emmanuil H. Georgoulis Emmanuil.Georgoulis@mcs.le.ac.uk

Paul Houston Paul.Houston@nottingham.ac.uk

Juha Virtanen jmv8@le.ac.uk



Abstract

We introduce a residual-based a posteriori error indicator for discontinuous Galerkin discretizations of the biharmonic equation with essential boundary conditions. We show that the indicator is both reliable and efficient with respect to the approximation error measured in terms of a natural energy norm, under minimal regularity assumptions. We validate the performance of the indicator within an adaptive mesh refinement procedure and show its asymptotic exactness for a range of test problems.

Journal Article Type Article
Journal IMA Journal of Numerical Analysis
Print ISSN 0272-4979
Publisher Oxford University Press (OUP)
Peer Reviewed Not Peer Reviewed
APA6 Citation Georgoulis, E. H., Houston, P., & Virtanen, J. An A Posteriori Error Indicator for Discontinuous Galerkin Approximations of Fourth Order Elliptic Problems. Manuscript submitted for publication
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf
Additional Information This article has been submitted for publication in IMA Journal of Numerical Analysis ©: 2008, Georgoulis, Emmanuil H. and Houston, Paul and Virtanen, Juha. Published by Oxford University Press. All rights reserved.

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Georgoulis_Houston_Virtanen_Aposteriori_for_DG_for_4th_order.pdf (306 Kb)
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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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