Atlas: Some useful techniques for pointwise and local error estimates of the quantities of interest in the finite element approximation by Thang Cao

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Computational Techniques and Applications Conference and Workshops - CTAC99
September 20-24, 1999
The Australian National University
Canberra, ACT, Australia

Organizers
Mike Osborne, Bob Gingold, Steve Roberts, David Harrar II, Thanh Tran, Bob Anderssen, Henry Gardner, Markus Hegland, Lutz Grosz

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Some useful techniques for pointwise and local error estimates of the quantities of interest in the finite element approximation
by
Thang Cao
School of Mathematics, University of NSW, Australia
Coauthors: D. W. Kelly (School of Mechanical and Manufacturing Engineering, University of NSW, Australia), M. Ainsworth (University Of Strathclyde, Scotland)

In this paper we review some existing techniques to obtain the pointwise and local a posteriori error estimates for the quantities of interest in the finite element approximations by using duality arguments. We also present a new approach to obtain the computable error bounds for the recovered pointwise quantities. The new method is extended to include the practically important case of non-homogeneous Dirichlet data. Existing methods require purely Neumann data, or the Dirichlet data to be homogeneous. The new techniques are developed here to provide computable error bounds on the genuine pointwise quantities and allow the use of non-homogeneous. The strength and weakness of each technique will be analysed and compared. The numerical experiments to justify our analysis will be presented.

Date received: July 29, 1999