Remarks on determining projections for stochastic dissipative equations

Discrete and Continuous Dynamical Systems

Volumn 5, Issue 1, 1999, Pages 197-214

  Berselli, Luigi C ^a   Flandoli, Franco ^a  

^a UNIVERSITY OF PISA   (Italy)

Author keywords

Determining projections; Random dynamical systems; Stochastic dissipative equations

Indexed keywords

EID: 0033477507     PISSN: 10780947     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (18)

1. A. Bensoussan and R. Temam, Equations stochastiques du type Navier-Stokes, J. Funct. Anal. 13 (1973), 195-22.
2. P.G. Ciarlet, The finite element method for elliptic problems, North-Holland, New York, 1978.
3. Ph. Clement, Approximation by Finite Element Functions Using Local Regularization, R.A.I.R.O. Anal. Numér. 9 (1975), 77-84.
4. P. Constantin and C. Foias, Navier-Stokes Equations, Chicago Lectures in Mathematics, Univ. of Chicago Press, 1988.
5. H. Crauel, A. Debussche, and F. Flandoli, Random Attractors, J. Dyn. Differ. Equations 9 (1997), no. 2, 307-341.
6. F. Flandoli and J.A. Langa, Determining Modes for Dissipative Random Dynamical Systems, J. Dyn. Differ. Equations To appear.
7. C. Foias and G. Prodi, Sur le Comportment Global des Solutions non Stationnaires des Équations de Navier-Stokes en Dimension 2, Rend. Sem. Mat. Univ. Padova 39 (1967), 1-34.
8. C. Foias and R. Temam, Determination of the solutions of the Navier-Stokes Equations by a Set of Nodal Values, Math. Comp. 43 (1984), no. 167, 117-133.
9. H. Crauel and F. Flandoli, Attractors for Random Dynamical Systems, Probab. Theory Relat. Fields 100 (1994), no. 3, 365-393.
10. M.J. Holst and E.S. Titi, Determining Projections and Functional for Weak Solutions of the Navier-Stokes equations, Recent developments in optimization theory and nonlinear analysis. AMS/IMU special session on optimization and nonlinear analysis (Y. Censor et al., ed.), Contemp. Math., vol. 104, American Mathematical Society, 1997, pp. 125-138.
11. J.L. Lions, Quelque méthodes de résolution des problemeœs aux limitex non-lineaires, Dunod Gauthier-Villars, 1969.
12. D.A. Jones and E.S. Titi, Determining Finite Volume Elements for the 2D Navier-Stokes Equations, Physica D 60 (1992), 165-174.
13. G. Da Prato and J. Zabczyk, Stochastic equations in infinite dimensions, Cambridge Univ. Press, 1992.
14. A. Quarteroni and A. Valli, Numerical Approximation of Partial Differential Equations, Springer series in Computational Mathematics, no. 23, Springer-Verlag, Berlin, 1994.
15. L.R. Scott and S. Zhang, Finite Element Interpolation of Nonsmooth Function Satisfying Boundary Conditions, Math. Comp. 54 (1990), no. 190, 483-493.
16. _, Higher Dimensional non-nested Multigrid Methods, Math. Comp. 58 (1992), 457-466.
17. R. Temam, Navier-Stokes Equations. Theory and Numerical Analysis, 3rd ed., North-Holland, 1984.
18. M.I. Vishik and A.V. Fursikov, Mathematical Problems of Statistical Hydromechanics, Kluver, Dordrecht, 1980.