Stability and convergence for the reform postprocessing Galerkin method *

Nonlinear Analysis: Real World Applications

Volumn 1, Issue 4, 2000, Pages 517-533

  Yinnian, He ^a   Mattheij, R M M ^b  

^a XI'AN JIAOTONG UNIVERSITY   (China)

^b EINDHOVEN UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

Convergence rate; Galerkin method; Navier stokes equations; Postprocessing Galerkin method; Stability

Indexed keywords

EID: 0034369956     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(99)00283-7     Document Type: Article

References (11)

1. J.B. Burie, M. Marion, Multilevel methods in space and time for the Navier-Stokes equations, SIAM J. Numer. Anal. 34(4) (1997) 1574-1599.
2. C. Devulder, M. Marion, E.S. Titi, On the rate of convergence of the nonlinear Galerkin methods, Math. Comput. 60(2) (1993) 495-514.
3. C. Foias, O. Manley, R. Temam, Modelling of the interaction of small and large eddies in two dimensional turbulent flows, Math. Modelling Numer. Anal. 22 (1988) 93-114.
4. B. Garcia-Archilla, J. Novo, E.S. Titi, Postprocessing the Galerkin method: A novel approach to approximate inertial manifolds, SIAM J. Numer. Anal. 35(3) (1998) 941-972.
5. B. Garcia-Archilla, J. Novo, E.S. Titi, An approximate inertial manifolds approach to postprocessing the Galerkin method for the Navier-Stokes equations, Math. Comput, in press.
6. He Yinnian, Li Kaitai, Convergence and stability of finite element nonlinear Galerkin method for the Navier-Stokes equations, Numer. Math. 79(1) (1998) 77-106.
7. He Yinnian, R.M.M. Mattheij, Reform Postprocessing Galerkin Method for the Navier-Stokes Equations, submitted for publication.
8. J.G. Heywood, R. Rannacher, On the question of turbulence modeling by appoximate inertial manifolds and the nonlinear Galerkin method, SIAM J. Numer. Anal. 30 (1993) 1603-1621.
9. M. Marion, R. Temam, Nonlinear Galerkin methods, SIAM J. Numer. Anal. 26 (1989) 1139-1157.
10. Shen Jie, Long time stability and convergence for fully discrete nonlinear Galerkin methods, Appl. Anal. 38 (1990) 201-229.
11. R. Temam, Infinite-Dimensional Dynamical Systems in Mechanics and Physics, Springer, New York, 1988.