Separation of variables in the Stokes problem application to its finite element multiscale approximation
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 28 (1994) no. 3, p. 243-266
@article{M2AN_1994__28_3_243_0,
     author = {Goubet, O.},
     title = {Separation of variables in the Stokes problem application to its finite element multiscale approximation},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {Dunod},
     volume = {28},
     number = {3},
     year = {1994},
     pages = {243-266},
     zbl = {0819.76044},
     mrnumber = {1275344},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_1994__28_3_243_0}
}
Goubet, O. Separation of variables in the Stokes problem application to its finite element multiscale approximation. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 28 (1994) no. 3, pp. 243-266. http://www.numdam.org/item/M2AN_1994__28_3_243_0/

[1] O. Axelsson and I. Gustafson, 1983, Preconditioning and two-level multigrid methods of arbitrary degree of approximation, Math. Comput., 40, 219-242. | MR 679442 | Zbl 0511.65079

[2] M. Bercovier and O. Pironneau, 1979, Error estimates for finite element solutions of the Stokes problem in the primitive variables, Numer. Math., 33, 211-224. | MR 549450 | Zbl 0423.65058

[3] F. Brezzi and M. Fortin, 1991, Mixed and Hybrid Finite Element Methods, Springer Series in Computational Mathematics, vol.15, Springer-Verlag, New York. | MR 1115205 | Zbl 0788.73002

[4] J. H. Bramble, J. E. Pasciak and J. Xu, 1990, Parallel multilevel preconditioners, Math. Comput., 55,1-22. | MR 1023042 | Zbl 0703.65076

[5] M. Chen and R. Temam, 1991, The incremental unknowns method, I, II, Applied Mathematics Letters. | MR 1101880 | Zbl 0726.65133

[6] P. Ciarlet, 1977, The Finite Element Method for Elliptic Problems, North-Holland. | Zbl 0383.65058

[7] A. Debussche and M. Marion, On the construction of families of approximate inertial manifolds, J. Diff. Equ., to appear. | MR 1187868 | Zbl 0760.34050

[8] I. Ekeland and R. Temam, 1976, Convex Analysis and Variational Problems, North-Holland, Amsterdam. | MR 463994 | Zbl 0322.90046

[9] I. Flahaut, 1991, Approximate inertial manifolds for the sine-Gordon equation, J. Diff. and Integ. Equ., 4, 1169-1194. | MR 1133751 | Zbl 0748.35039

[10] C. Foias, O. Manley and R. Temam, 1988, Modelling of the interaction of small and large eddies in two-dimensional turbulent flows, Math, Model. Numer. Anal, 22, 93-114. | Numdam | MR 934703 | Zbl 0663.76054

[11] C. Foias, . S Sell and R. Temam, 1988, Inertial manifolds for nonlinear evolutionary equations, J. Diff. Equ., 73,309-353. | MR 943945 | Zbl 0643.58004

[12] V. Girault and P. A. Raviart, 1986, Finite Element Methods for Navier-Stokes Equations, Springer Series in Computational Mathematics, vol. 5, Springer-Verlag, New York. | MR 851383 | Zbl 0585.65077

[13] O. Goubet, 1992, Construction of approximate inertial manifolds using wavelets, SIAM J. Math. Anal., 23,1455-1481. | MR 1185638 | Zbl 0770.35003

[14] O. Goubet, 1992, Separation des variables dans le probleme de Stokes. Application à son approximation multiéchelles éléments finis, C. R. Acad. Sci.Paris, 315, Série I, 1315-1318. | MR 1194543 | Zbl 0763.76043

[15] P. Grisvard, 1980, Boundary Value Problems in Non-smooth Domains, Univ.of Maryland, Départ, of Math., Lecture Notes n° 19.

[16] M. Marion and R. Temam, 1989, Nonlinear Galerkin methods, SIAM J. Numer. Anal., 26, 1139-1157. | MR 1014878 | Zbl 0683.65083

[17] M. Marion and R. Temam, 1990, Nonlinear Galerkin methods, the finite elements case, Numer. Math., 57,1-22. | MR 1057121 | Zbl 0702.65081

[18] F. Pascal, 1992, Thesis, Université de Paris-Sud.

[19] K. Promislow and R. Temam, Localization and approximation of attractors for the Ginzburg-Landau equation, J. Dynamic and Diff. Equ., to appear. | MR 1129558 | Zbl 0751.34036

[20] R. Temam, 1988, Infinite-Dimensional Dynamical Systems in Mechanics and Physics, Appl. Math. Sci., 68. | MR 953967 | Zbl 0662.35001

[21] R. Temam, 1989, Attractors for the Navier-Stokes equations, localization and approximation, J. Fac. Sci. Tokyo, Sec. IA, 36, 629-647. | MR 1039488 | Zbl 0698.58040

[22] R. Temam, 1990, Inertial manifolds and multigrid methods, SIAM J. Math. Anal., 21, 154-178. | MR 1032732 | Zbl 0715.35039

[23] R. Temam, 1984, Navier-Stokes Equations, 3rd ed., North-Holland, Amsterdam. | MR 769654 | Zbl 0568.35002

[24] R. Verfürth, 1984, Error estimates for a mixed finite element approximation of the Stokes equations, RAIRO Numer. Anal., 18, 175-182. | Numdam | MR 743884 | Zbl 0557.76037

[25] H. Yserentant, 1986, On the multi-level spliting of finite element spaces, Numer. Math., 49, 379-412. | Zbl 0608.65065