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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)



Estimates of deviations from exact solutions for boundary-value problems with incompressibility condition

Author: S. Repin
Translated by: the author
Original publication: Algebra i Analiz, tom 16 (2004), nomer 5.
Journal: St. Petersburg Math. J. 16 (2005), 837-862
MSC (2000): Primary 35J50, 65N15, 74G45
Published electronically: September 21, 2005
MathSciNet review: 2106670
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Abstract: Methods of estimating the difference between exact and approximate solutions are considered for boundary-value problems in spaces of solenoidal functions. The estimates obtained apply to any functions in the energy space of the respective problem, and their computation requires solving only finite-dimensional problems. In the paper, two different methods are considered: one involves variational formulations and duality theory, and in the other, estimates are obtained from the integral identities that define generalized solutions of the problems in question. It is shown that estimates of deviations from an exact solution must include an additional penalty term with a factor determined by the constant in the Ladyzhenskaya-Babuska-Brezzi condition.

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Keywords: Boundary-value problems with incompressibility condition, \emph{a posteriori} error estimates, Stokes problem
Received by editor(s): December 10, 2003
Published electronically: September 21, 2005
Additional Notes: This work was supported by the Civilian Research and Development Foundation (grant no. RU-M1-2596-ST-04) and by the Russian Ministry of Education (grant no. E02-1.0-55)
Dedicated: Dedicated to the memory of O. A. Ladyzhenskaya
Article copyright: © Copyright 2005 American Mathematical Society

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