Geodesic
Functional a posteriori estimates
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 38, Tome 348 (2007), pp. 147-164 Cet article a éte moissonné depuis la source Math-Net.Ru

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In the paper, we present a new way of the derivation of computable estimates for the difference between exact solutions of elliptic variational inequalities and arbitrary functions in the respective energy space that satisfy the main (Dirichlét) boundary conditions. Unlike the method exposed in [11, 18], we derive the estimates by certain transformations of variational inequalities without the attraction of duality arguments. For linear elliptic and parabolic problems this method was suggested in [16, 17]. In the present paper, we consider two different types of variational inequalities (also called variational inequalities of the first and second kinds [10]). The techniques discussed can be applied to other nonlinear problems related to variational inequalities. 
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     author = {S. I. Repin},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2007_348_a5/}
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S. I. Repin. Functional a posteriori estimates. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 38, Tome 348 (2007), pp. 147-164. http://geodesic.mathdoc.fr/item/ZNSL_2007_348_a5/

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[3] M. Bildhauer, M. Fuchs, and S. Repin, “A functional type a posteriori error analysis of the functional type for the Ramberg–Osgood model”, ZAMM (to appear)

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[18] S. Repin, “Estimates of deviations from exact solutions of elliptic variational inequalities”, Zap. Nauchn. Semin. POMI, 271, 2000, 188–203 | MR | Zbl

[19] S. Repin and J. Valdman, “A posteriori error estimates for problems with nonlinear boundary conditions”, J. Numer. Math. (to appear)

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