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

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

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
• Peer Reviewed: Not Peer Reviewed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.