Geodesic
Local a posteriori estimates for the Stokes problem
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 36, Tome 318 (2004), pp. 233-245 Cet article a éte moissonné depuis la source Math-Net.Ru

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In the paper, computable estimates of the difference between the exact solution of the Stokes problem and an approximation from the respective energy class are obtained. Estimates are presented in terms of local norms and linear functionals. Certain generalizations to some nonlinear problems are discussesd. 
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     title = {Local a~posteriori estimates for the {Stokes} problem},
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S. I. Repin. Local a posteriori estimates for the Stokes problem. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 36, Tome 318 (2004), pp. 233-245. http://geodesic.mathdoc.fr/item/ZNSL_2004_318_a11/

[1] M. Ainsworth, J. T. Oden, A posteriori error estimation in finite element analysis, Wiley, 2000 | MR | Zbl

[2] C. Carstensen, S. Bartels, “Each averaging technique yields reliable a posteriori error control in FEM on unstructured grids. I: Low order conforming, nonconforming, and mixed FEM”, Math. Comp., 71:239 (2002), 945–969 | DOI | MR | Zbl

[3] W. Bangerth, R. Rannacher, Adaptive finite element methods for differential equations, Birkhäuser, Berlin, 2003 | MR | Zbl

[4] M. Feistauer, Mathematical methods in fluid dynamics, Longman, Harlow, 1993 | Zbl

[5] S. Korotov, P. Neittaanmaki, S. Repin, “A posteriori error estimation of goal-oriented quantities by the superconvergence patch recovery”, J. Numer. Math., 11:1 (2003), 33–59 | MR | Zbl

[6] M. Fuchs, G. A. Seregin, Variational methods for problems from plasticity theory and for generalized Newtonian fluids, Lect. Notes Math., 1749, 2000 | MR | Zbl

[7] Girault V., Raviart P. A., Finite element approximation of the Navier–Stokes equations, Lecture Notes Math., 749, 1979 | MR | Zbl

[8] O. A. Ladyzhenskaya, The mathematical theory of viscous incompressible flow, Gordon and Breach, New York, 1969 | MR | Zbl

[9] O. A. Ladyzhenskaya, On nonlinear problems of continuum mechanics, Proc. Internat. Congr. Math. (Moscow, 1966), Amer. Math. Soc. Transl. (2), 70, 1968 | Zbl

[10] O. A. Ladyzhenskaya, “On some modifications of the Navier–Stokes equations for large gradients of velocity”, Zap. Nauchn. Sem. LOMI, 7, 1968, 126–154 | MR | Zbl

[11] S. I. Repin, “A posteriori estimates in local norms”, J. Math. Sci., 124:3 (2004), 5026–5035 | DOI | MR | Zbl

[12] S. I. Repin, “Aposteriori estimates for the Stokes problem”, J. Math. Sci., 109:5 (2002), 1950–1964 | DOI | MR

[13] S. Repin, “Estimates of deviations for generalized Newtonian fluids”, Zap. Nauchn. Semin. POMI, 288, 2002, 178–203 | MR | Zbl

[14] S. Repin, “A posteriori estimates of the accuracy of approximate solutions of boundary-value problems with incompressibility condition”, Algebra Analiz, 16:5 (2004), 124–161 | MR | Zbl

[15] S. Repin, S. Sauter, A. Smolianski, “A posteriori error estimation for the Dirichlet problem with account of the error in approximation of boundary conditions”, Computing, 2003, no. 3, 147–168 | MR

[16] R. Verfürth, “A posteriori error estimators for the Stokes equations”, Numer. Math., 55 (1989), 309–326 | DOI | MR

[17] O. C. Zienkiewicz, J. Z. Zhu, “A simple error estimator and adaptive procedure for practical engineering analysis”, Internat. J. Numer. Meth. Engrg., 24 (1987), 337–357 | DOI | MR | Zbl