S. Korotov, P. Neittaanmki, S. Repin
A posteriori error estimation of goal-oriented quantities by the superconvergence patch recovery
The paper is concerned with a posteriori error estimation in terms of special problem-oriented
quantities. In many practically interesting cases, such a quantity is represented as a linear
functional that controls the behavior of a solution in certain subdomains, along some lines, or at especially
interesting points. The method of estimating quantities of interest is usually based upon the
analysis of the adjoint boundary-value problem, whose right hand side is formed by the considered
linear functional. On this way, we propose a new effective modus operandi. It is based on two principles:
(a) the original and adjoint problems are solved on non-coinciding meshes, and (b) the term
presenting the product of gradients of errors of the primal and adjoint problems is estimated by using
the 'gradient averaging' technique. Numerical tests confirm high effectivity of this approach.
Journal of Numerical Mathematics, Walter de Gruyter
Print ISSN: 1570-2820
Volume: 11, 03/2003
Pages: 33 - 59
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