Please use this identifier to cite or link to this item: doi:10.22028/D291-26518
Title: Estimates of the deviations from the exact solutions for variational inequalities describing the stationary flow of certain viscous incompressible fluids
Author(s): Fuchs, Martin
Repin, Sergey
Language: English
Year of Publication: 2009
Free key words: variational inequalities
viscous incompressible fluids
generalized Newtonian fluids
DDC notations: 510 Mathematics
Publikation type: Other
Abstract: This paper is concerned with computable and guaranteed upper bounds of the difference between exact solutions of variational inequalities arising in the theory of viscous fluids and arbitrary approximations in the corresponding energy space. Such estimates (also called error majorants of functional type) have been derived for the considered class of nonlinear boundary value problems in [11] with the help of variational methods based on duality theory from convex analysis. In the present paper it is shown that error majorants can be derived in a different way by certain transformations of the variational inequalities that define generalized solutions. The error bounds derived by this techniques for the velocity function differ from those obtained by the variational method. These estimates involve only global constants coming from Korn and Friedrichs type inequalities, which are not difficult to evaluate in case of Dirichlet boundary conditions. For the case of mixed boundary conditions, we also derive another form of the estimate which contains only one constant coming from the following assertion: the L^{2} norm of a vector valued function from H^{1}(\Omega) in the factor-space generated by the equivalence with respect to rigid motions is bounded by the L^{2} norm of the symmetric part of the gradient tensor. Since for some ”simple” domains like squares or cubes, the constants in this inequality can be found analytically (or numerically), we obtain a unified form of an error majorant for any domain that admits a decomposition into such subdomains.
Link to this record: urn:nbn:de:bsz:291-scidok-47693
Series name: Preprint / Fachrichtung Mathematik, Universität des Saarlandes
Series volume: 235
Date of registration: 6-Jun-2013
Faculty: MI - Fakultät für Mathematik und Informatik
Department: MI - Mathematik
Collections:SciDok - Der Wissenschaftsserver der Universität des Saarlandes

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