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

Georgoulis, Emmanuil H. and Houston, Paul and Virtanen, Juha (2008) An A Posteriori Error Indicator for Discontinuous Galerkin Approximations of Fourth Order Elliptic Problems. IMA Journal of Numerical Analysis . (Submitted)

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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.

Item Type:Article
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.
Schools/Departments:Faculty of Science > School of Mathematical Sciences
ID Code:913
Deposited By:Houston, Paul
Deposited On:09 Jun 2008 10:08
Last Modified:24 Jun 2011 15:25

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