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 Zap. Nauchn. Sem. POMI, 2009, Volume 370, Pages 132–150 (Mi znsl3535)

Estimates of deviations from exact solutions of variational problems with linear growth functionals

S. I. Repin

St. Petersburg Department of Steklov Mathematical Institute RAS, St. Petersburg, Russia

Abstract: In this paper, we derive estimates of deviations from exact solutions of variational problems with linear growth functionals. Since original variational problem may have no minimizer in a reflexive Banach space, the estimates are presented in terms of the dual problem. We prove the consistency of these estimates and obtain their computationally convenient forms. Bibl. – 36 titles.

Key words and phrases: a posteriori error estimates, duality theory, variational problems, linear growth functionals.

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English version:
Journal of Mathematical Sciences (New York), 2010, 166:1, 75–85

UDC: 517.9
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Citation: S. I. Repin, “Estimates of deviations from exact solutions of variational problems with linear growth functionals”, Boundary-value problems of mathematical physics and related problems of function theory. Part 40, Zap. Nauchn. Sem. POMI, 370, POMI, St. Petersburg, 2009, 132–150; J. Math. Sci. (N. Y.), 166:1 (2010), 75–85

Citation in format AMSBIB
\Bibitem{Rep09} \by S.~I.~Repin \paper Estimates of deviations from exact solutions of variational problems with linear growth functionals \inbook Boundary-value problems of mathematical physics and related problems of function theory. Part~40 \serial Zap. Nauchn. Sem. POMI \yr 2009 \vol 370 \pages 132--150 \publ POMI \publaddr St.~Petersburg \mathnet{http://mi.mathnet.ru/znsl3535} \transl \jour J. Math. Sci. (N. Y.) \yr 2010 \vol 166 \issue 1 \pages 75--85 \crossref{https://doi.org/10.1007/s10958-010-9846-8} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-77949296650} 

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. Fuchs M., Repin S., “A posteriori error estimates for the approximations of the stresses in the Hencky plasticity problem”, Numer. Funct. Anal. Optim., 32:6 (2011), 610–640
2. Haslinger J., Repin S., Sysala S., “A reliable incremental method of computing the limit load in deformation plasticity based on compliance: Continuous and discrete setting”, J. Comput. Appl. Math., 303 (2016), 156–170
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