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Estimateurs a posteriori d’erreur pour le calcul adaptatif d’écoulements quasi-Newtoniens. (A posteriori error estimators for adaptive calculation of quasi-Newtonian flows). (French) Zbl 0712.76068
Summary: We study a posteriori error estimators for the mixed finite element approximation of some quasi-Newtonian flows (fluids whose viscosity varies with the second invariant of the rate of deformation tensor). These estimators necessitate only the evaluation of the local residual of the finite element solution. They can be used in a self-adaptive mesh- refinement process.

MSC:
76M10 Finite element methods applied to problems in fluid mechanics
76A05 Non-Newtonian fluids
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[1] E. ABDALASS [ 1987], Résolution Performante du Problème de Stokes par Mini-Élément, Maillage Auto-Adaptatifs et Méthodes Multigrilles Applications.Thèse de Doctorat, École Centrale de Lyon.
[2] E. ABDALASS, J. F. MAITRE & F. MUSY [ 1987], A finite element solution of Stokes problem with an adaptive procedure, lst ICIAM Paris. · Zbl 0616.65104
[3] 0 I. BABUSKA & W. C. RHEINBOLTD [ 1978] a), Error Estimates for Adaptative Finite Element Computations. SIAM J. Numer. Anal. Vol. 15, n^\circ 4. Zbl0398.65069 MR483395 · Zbl 0398.65069 · doi:10.1137/0715049
[4] I. BABUSKA & W. C. RHEINBOLTD [ 1978] b), A Posteriori Error Estimates for the Finite Element Method. Int. J. Numer. Meth. Engng., 12, 1597-1615. Zbl0396.65068 · Zbl 0396.65068 · doi:10.1002/nme.1620121010
[5] I. BABUSKA & W. C. RHEINBOLTD [ 1979], Analysis of Optimal Finite Element Meshes in R. Math. of Computation, 33, 435-463. Zbl0431.65055 MR521270 · Zbl 0431.65055 · doi:10.2307/2006290
[6] R. E. BANK [ 1986], Analysis of a Local a posteriori Error Estimate for Elliptic Equations. Dans < Accuracy Estimates and Adaptive Refinements in Finite Element Computations > , Edit. Babuska, L, Zienkiewicz, O. C, Gago, J. et Oliveira, A. Zbl0663.65001 MR879445 · Zbl 0663.65001
[7] R. E. BANK & A. H. SHERMAN [ 1980], The use of Adaptive Grid Refinement for Badly Behaved Elliptic Partial Differential Equations. Math, and Computer XXII, pp. 18-24. Zbl0434.35008 · Zbl 0434.35008 · doi:10.1016/0378-4754(80)90098-1
[8] J. BARANGER & H. EL AMRI [ 1989], A posteriori error estimators for mixed finite element approximation of some quasi-newtonian flows. Invited lecture at the Workshop on innovative finite element methods. Rio de Janeiro Nov. 27 to Dec. lst. · Zbl 0770.76034
[9] J. BARANGER & K. NAJIB [ 1989], Analyse numérique d’une méthode d’éléments finis mixtes vitesse-pression pour le calcul d’écoulements quasi-newtoniens. 2e Congrès Franco-Chilien et Latino-Américain de mathématiques Appliquées, Santiago de Chile, décembre. Zbl0752.76006 · Zbl 0752.76006
[10] C. BERNARDI [ 1984], Optimal Finite Element Interpolation on Curved Domains. Publications du Laboratoire d’Analyse Numérique de l’Université Pierre et Marie Curie, n^\circ 17. Zbl0678.65003 · Zbl 0678.65003 · doi:10.1137/0726068
[11] P. G. CIARLET [ 1978], The Finite Element Method for Elliptic Problems. Studies in Mathematics and its Applications, Volume 4, North-Holland. Zbl0383.65058 MR520174 · Zbl 0383.65058
[12] Ph. CLÉMENT [ 1975], Approximation by Finite Element Functions using Local Regularization. R.A.I.R.O. n^\circ 2, pp. 77-84. Zbl0368.65008 MR400739 · Zbl 0368.65008 · eudml:193271
[13] P. GEORGET [ 1985], Contribution à l’étude des équations de Stokes à viscosité variable. Thèse de Doctorat. Université de Lyon I.
[14] V. GIRAULT, P. A. RAVIART [ 1986], Finite Element Methods for Navier-Stokes Equations. Theory and Algorithms. Amsterdam, North-Holland. Zbl0585.65077 MR851383 · Zbl 0585.65077
[15] R. GLOWINSKI, A. MARROCCO [ 1975], Sur l’approximation par éléments finis d’ordre 1 et la résolution par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. R-2 R.A.I.R.O. Analyse Numérique, pp. 41-76. Zbl0368.65053 MR388811 · Zbl 0368.65053 · eudml:193269
[16] K. NAJIB [ 1988], Analyse Numérique de Modèles d’Écoulements Quasi-Newtoniens. Thèse de Doctorat. Université de Lyon I.
[17] J. T. ODEN, L. DEMKOWICZ, Ph. DELVOO & T. STROUBOULIS [ 1986], Adaptive Methods for Problems in Solid and Fluid Mechanics. Dans < Accuracy Estimates and Adaptive Refinements in Finite Element Computations > , Edit. Babuska, L, Zienkiewicz, O. C, Gago, J. et Oliveira, A. MR879442
[18] M. C. RIVARA [ 1984], Adaptive Multigrid Software for the Finite Element Method. PhD thesis University Leuven, 1984. · Zbl 0578.65112
[19] I. G. ROSENBERG & F. STENGER [ 1975], A lower bound on the angles of triangles constructed by bisecting the logest side. Math. Comp. 29, pp. 390-395, 1975 Zbl0302.65085 MR375068 · Zbl 0302.65085 · doi:10.2307/2005558
[20] B. SCHEURER [ 1977], Existence et approximation de points selles pour certains problèmes non linéaires. R.A.I.R.O., Volume 11, n^\circ 4, Analyse Numérique, pp. 369-400. Zbl0371.65025 MR464014 · Zbl 0371.65025 · eudml:193308
[21] R. VERFÜRTH [ 1989], A posteriori error estimators for the Stokes equations. Numerische Mathematik. Volume 55, n^\circ 3, 1989, pp. 309-325. Zbl0674.65092 MR993474 · Zbl 0674.65092 · doi:10.1007/BF01390056 · eudml:133357
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