Separation of variables in the Stokes problem application to its finite element multiscale approximation

 Access to full text

 Full (PDF)

1. [1] O. AXELSSON and I. GUSTAFSON, 1983, Preconditioning and two-level multigrid methods of arbitrary degree of approximation, Math. Comput., 40, 219-242. Zbl0511.65079MR679442
2. [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. Zbl0423.65058MR549450
3. [3] F. BREZZI and M. FORTIN, 1991, Mixed and Hybrid Finite Element Methods, Springer Series in Computational Mathematics, vol.15, Springer-Verlag, New York. Zbl0788.73002MR1115205
4. [4] J. H. BRAMBLE, J. E. PASCIAK and J. Xu, 1990, Parallel multilevel preconditioners, Math. Comput., 55,1-22. Zbl0703.65076MR1023042
5. [5] M. CHEN and R. TEMAM, 1991, The incremental unknowns method, I, II, Applied Mathematics Letters. Zbl0726.65133MR1101880
6. [6] P. CIARLET, 1977, The Finite Element Method for Elliptic Problems, North-Holland. Zbl0383.65058
7. [7] A. DEBUSSCHE and M. MARION, On the construction of families of approximate inertial manifolds, J. Diff. Equ., to appear. Zbl0760.34050MR1187868
8. [8] I. EKELAND and R. TEMAM, 1976, Convex Analysis and Variational Problems, North-Holland, Amsterdam. Zbl0322.90046MR463994
9. [9] I. FLAHAUT, 1991, Approximate inertial manifolds for the sine-Gordon equation, J. Diff. and Integ. Equ., 4, 1169-1194. Zbl0748.35039MR1133751
10. [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. Zbl0663.76054MR934703
11. [11] C. FOIAS, . S SELL and R. TEMAM, 1988, Inertial manifolds for nonlinear evolutionary equations, J. Diff. Equ., 73,309-353. Zbl0643.58004MR943945
12. [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. Zbl0585.65077MR851383
13. [13] O. GOUBET, 1992, Construction of approximate inertial manifolds using wavelets, SIAM J. Math. Anal., 23,1455-1481. Zbl0770.35003MR1185638
14. [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. Zbl0763.76043MR1194543
15. [15] P. GRISVARD, 1980, Boundary Value Problems in Non-smooth Domains, Univ.of Maryland, Départ, of Math., Lecture Notes n° 19. 
16. [16] M. MARION and R. TEMAM, 1989, Nonlinear Galerkin methods, SIAM J. Numer. Anal., 26, 1139-1157. Zbl0683.65083MR1014878
17. [17] M. MARION and R. TEMAM, 1990, Nonlinear Galerkin methods, the finite elements case, Numer. Math., 57,1-22. Zbl0702.65081MR1057121
18. [18] F. PASCAL, 1992, Thesis, Université de Paris-Sud. 
19. [19] K. PROMISLOW and R. TEMAM, Localization and approximation of attractors for the Ginzburg-Landau equation, J. Dynamic and Diff. Equ., to appear. Zbl0751.34036MR1129558
20. [20] R. TEMAM, 1988, Infinite-Dimensional Dynamical Systems in Mechanics and Physics, Appl. Math. Sci., 68. Zbl0662.35001MR953967
21. [21] R. TEMAM, 1989, Attractors for the Navier-Stokes equations, localization and approximation, J. Fac. Sci. Tokyo, Sec. IA, 36, 629-647. Zbl0698.58040MR1039488
22. [22] R. TEMAM, 1990, Inertial manifolds and multigrid methods, SIAM J. Math. Anal., 21, 154-178. Zbl0715.35039MR1032732
23. [23] R. TEMAM, 1984, Navier-Stokes Equations, 3rd ed., North-Holland, Amsterdam. Zbl0568.35002MR769654
24. [24] R. VERFÜRTH, 1984, Error estimates for a mixed finite element approximation of the Stokes equations, RAIRO Numer. Anal., 18, 175-182. Zbl0557.76037MR743884
25. [25] H. YSERENTANT, 1986, On the multi-level spliting of finite element spaces, Numer. Math., 49, 379-412. Zbl0608.65065