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Strathprints serves world leading Open Access research by the University of Strathclyde, including research by the Strathclyde Institute of Pharmacy and Biomedical Sciences (SIPBS), where research centres such as the Industrial Biotechnology Innovation Centre (IBioIC), the Cancer Research UK Formulation Unit, SeaBioTech and the Centre for Biophotonics are based.

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A posteriori error estimators and adaptivity for finite element approximation of the non-homogeneous dirichlet problem

Ainsworth, Mark and Kelly, Donald W. (2001) A posteriori error estimators and adaptivity for finite element approximation of the non-homogeneous dirichlet problem. Advances in Computational Mathematics, 15 (1-4). pp. 3-23. ISSN 1019-7168

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Abstract

Techniques are developed for a posteriori error analysis of the non-homogeneous Dirichlet problem for the Laplacian giving computable error bounds for the error measured in the energy norm. The techniques are based on the equilibrated residual method that has proved to be reliable and accurate for the treatment of problems with homogeneous Dirichlet data. It is shown how the equilibrated residual method must be modified to include the practically important case of non-homogeneous Dirichlet data. Explicit and implicit a posteriori error estimators are derived and shown to be efficient and reliable. Numerical examples are provided illustrating the theory.