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A posteriori error identities for nonlinear variational problems

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Neittaanmäki, P., & Repin, S. (2015). A posteriori error identities for nonlinear variational problems. Annals of the Acacemy of Romanian Scientists : Mathematics and Its Applications, 7(1), 157-172. http://www.mathematics-and-its-applications.com/preview/june2015/data/articol10.pdf
Published in
Annals of the Acacemy of Romanian Scientists : Mathematics and Its Applications
Authors
Neittaanmäki, Pekka |
Repin, Sergey
Date
2015
Discipline
TietotekniikkaMathematical Information Technology
Copyright
© the Authors & Annals of the Acacemy of Romanian Scientists, 2015. This is an open access article published by Academy of Romanian Scientists.

 
A posteriori error estimation methods are usually developed in the context of upper and lower bounds of errors. In this paper, we are concerned with a posteriori analysis in terms of identities, i.e., we deduce error relations, which holds as equalities. We discuss a general form of error identities for a wide class of convex variational problems. The left hand sides of these identities can be considered as certain measures of errors (expressed in terms of primal/dual solutions and respective approximations) while the right hand sides contain only known approximations. Finally, we consider several examples and show that in some simple cases these identities lead to generalized forms of the Prager-Synge and Mikhlin’s error relations. Also, we discuss particular cases related to power growth functionals and to the generalized Stokes problem.
Publisher
Academy of Romanian Scientists
ISSN Search the Publication Forum
2066-5997
Keywords
estimates of deviations from the exact solution convex variation problems error measures for nonlinear problems

Original source
http://www.mathematics-and-its-applications.com/preview/june2015/data/articol10.pdf

URI

http://urn.fi/URN:NBN:fi:jyu-201607063511

Publication in research information system

https://converis.jyu.fi/converis/portal/detail/Publication/24767805

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