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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

PAUL HOUSTON PAUL.HOUSTON@NOTTINGHAM.AC.UK
Professor of Computational and Applied Maths

Juha Virtanen



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.

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

Journal Article Type Article
Deposit Date Jun 9, 2008
Publicly Available Date Mar 28, 2024
Peer Reviewed Not Peer Reviewed
Public URL https://nottingham-repository.worktribe.com/output/1015794
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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