Separation of variables in the Stokes problem application to its finite element multiscale approximation
ESAIM: Modélisation mathématique et analyse numérique, Tome 28 (1994) no. 3, pp. 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: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {243--266},
     publisher = {AFCET - Gauthier-Villars},
     address = {Paris},
     volume = {28},
     number = {3},
     year = {1994},
     mrnumber = {1275344},
     zbl = {0819.76044},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_1994__28_3_243_0/}
}
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Goubet, O. Separation of variables in the Stokes problem application to its finite element multiscale approximation. ESAIM: 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 | Zbl

[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 | Zbl

[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 | Zbl

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

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

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

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

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

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

[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 | Zbl

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

[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 | Zbl

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

[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 | Zbl

[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 | Zbl

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

[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 | Zbl

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

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

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

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

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

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