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Journal of Numerical Mathematics

Editor-in-Chief: Hoppe, Ronald H. W. / Kuznetsov, Yuri

Managing Editor: Olshanskii, Maxim

Editorial Board Member: Benzi, Michele / Brenner, Susanne C. / Carstensen, Carsten / Dryja, M. / Feistauer, Miloslav / Glowinski, R. / Lazarov, Raytcho / Nataf, Frédéric / Neittaanmaki, P. / Bonito, Andrea / Quarteroni, Alfio / Guzman, Johnny / Rannacher, Rolf / Repin, Sergey I. / Shi, Zhong-ci / Tyrtyshnikov, Eugene E. / Zou, Jun / Simoncini, Valeria / Reusken, Arnold

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Online
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1569-3953
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Volume 11, Issue 1 (Mar 2003)

Issues

A posteriori error estimation of goal-oriented quantities by the superconvergence patch recovery

S. Korotov
  • Department of Mathematical Information Technology, University of Jyväskylä, P. O. Box 35, FIN–40014 Jyväskylä, Finland
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ P. Neittaanmäki
  • Department of Mathematical Information Technology, University of Jyväskylä, P. O. Box 35, FIN–40014 Jyväskylä, Finland
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ S. Repin
  • Department of Mathematical Information Technology, University of Jyväskylä, P. O. Box 35, FIN–40014 Jyväskylä, Finland
  • V. A. Steklov Institute of Mathematics in St.-Petersburg, St.-Petersburg, 191011, Fontanka 27, Russia
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar

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.

Key Words: a posteriori error estimation,; quantities of interest,; finite element method,; differential equation of elliptic type,; superconvergence

About the article

Published in Print: 2003-03-01


Citation Information: Journal of Numerical Mathematics jnma, ISSN (Online) 1569-3953, ISSN (Print) 1570-2820, DOI: https://doi.org/10.1515/156939503322004882.

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