Attractors and error estimates for discretizations of incompressible navier-stokes equations

SIAM Journal on Numerical Analysis

Volumn 33, Issue 4, 1996, Pages 1451-1472

  Yan, Yin ^a  

^a VIRGINIA POLYTECHNIC INSTITUTE AND STATE UNIVERSITY   (United States)

Author keywords

Absorbing inequalities; Attractors; Error estimates; Error estimates with tolerance; Finite difference; Hausdorff metric; Trajectories

Indexed keywords

EID: 0346275725     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142993248092     Document Type: Article

References (26)

1. J. CÉA (1964), Approximation variationnelle des problèmes aux limits, Ann. Inst. Fourier, 14, pp. 345-444.
2. P. CONSTANTIN AND C. FOIAS (1988), Navier-Stokes Equations, Univ. of Chicago Press, Chicago.
3. C. FOIAS AND R. TEMAM (1988), Determination of the solutions of the Navier-Stokes equations by a set of nodal values, Math. Comp., 43, pp. 117-133.
4. C. FOIAS AND E. S. TITI (1991), Determining nodes, finite difference schemes and inertial manifolds, Nonlinearity, 4, pp. 135-153.
5. J. GOODMAN AND P. LAX (1988), On dispersive difference schemes, I, Comm. Pure Appl. Math., 41, pp. 591-613.
6. J. K. HALE, X.-B. LIN, AND G. RAUGEL (1988), Upper semicontinuity of attractors for approximations of semigroups and partial differential equations, Math. Comp., 50, pp. 89-123.
7. J. G. HEYWOOD AND R. RANNACHER (1982), Finite element approximations of the nonstationary Navier-Stokes problem. I: Regularity of solutions and second-order error estimates for spatial discretization, SIAM J. Numer. Anal., 19, pp. 275-311.
8. _ (1986), Finite element approximations of the nonstationary Navier-Stokes problem, II: Stability of solutions and error estimates uniform in time, SIAM J. Numer. Anal., 23, pp. 750-777.
9. _ (1988), Finite element approximations of the nonstationary Navier-Stokes problem, III: Smoothing property and higher-order error estimates for spatial discretization, SIAM J. Numer. Anal., 25, pp. 489-512.
10. _ (1990), Finite element approximations of the nonstationary Navier-Stokes problem, IV: Error estimates for second-order time discretization, SIAM J. Numer. Anal., 27, pp. 353-384.
11. F. JOHN (1952), On integration of parabolic equations by difference methods, Comm. Pure Appl. Math., 5, pp. 155-211.
12. C. JOHNSON, R. RANNACHER, AND M. BOMAN (1995), Numerics and hydrodynamic stability: Towards error control in CFD, SIAM J. Numer. Anal., 32, pp. 1058-1079.
13. O. A. LADYZHENSKAYA (1969), The Mathematical Theory of Viscous Incompressible Flow, Gordon and Breach, New York.
14. L. MA (1990), Large Time Study of Finite Element Methods for 2D Navier-Stokes Equations, IMA preprint No. 739.
15. V. PLISS AND G. R. SELL (1991), Perturbations of attractors of differential equations, J. Differential Equations, 92, pp. 100-124.
16. G. RAUGEL AND G. R. SELL (1989), Équations de Navier-Stokes dans des domains minces endimension trois: Régularité globale, C. R. Acad. Sci. Paris, 309, pp. 299-303.
17. _ (1993), Navier-Stokes equations in thin 3D domains: Global regularity of solutions I, J. Amer. Math. Soc., 6, pp. 503-568.
18. _ (1994), Navier-Stokes equations in thin 3D domains II: Global regularity of spatially periodic solutions, in Proc. College de France.
19. R. RAUTMAN (1980), On the convergence rate of nonstationary Navier-Stokes approximations, Springer Lect. Notes Math., 771, pp. 425-449.
20. F. STRANG (1964), Accurate partial difference methods II. Non-linear problems, Numer. Math., 6, pp. 37-46.
21. R. TEMAM (1983), Navier-Stokes Equations and Nonlinear Functional Analysis, Society for Industrial and Applied Mathematics, Philadelphia.
22. _ (1984), Navier-Stokes Equations, 3rd ed., Elsevier, New York.
23. _ (1988), Infinite Dimensional Dynamical Systems in Mechanics and Physics, Springer-Verlag, New York.
24. _ (1990), Inertial manifold and multigrid methods, SIAM J. Math. Anal., 21, pp. 154-178.
25. Y. YAN (1992), Dimensions of attractors for discretizations for Navier-Stokes equations, J. Dynamics Differential Equations, 4, pp. 275-340.
26. _ (1993), Attractors and dimensions for discretizations of a weakly damped Schrödinger equations and a Sine-Gorden equations, Nonlinear Anal. 20, pp. 1417-1452.