A small eddy correction method for nonlinear dissipative evolutionary equations

SIAM Journal on Numerical Analysis

Volumn 41, Issue 3, 2003, Pages 1101-1130

  Hou, Yanren ^a   Li, Kaitai ^a  

^a XI'AN JIAOTONG UNIVERSITY   (China)

Author keywords

Dissipative equations; Multilevel method; Newton iteration; Spectral methods

Indexed keywords

APPROXIMATION THEORY; ERROR ANALYSIS; GALERKIN METHODS; INTEGRATION; ITERATIVE METHODS; MATHEMATICAL OPERATORS; NAVIER STOKES EQUATIONS; NUMERICAL METHODS; VELOCITY MEASUREMENT;

DISSIPATIVE EQUATIONS; MULTILEVEL METHODS; NEWTON ITERATIONS; SPECTRAL METHODS;

NONLINEAR EQUATIONS;

EID: 3142782794     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142901396375     Document Type: Article

References (22)

1. A. AIT OU AMMI AND M. MARION, Nonlinear Galerkin methods and mixed finite elements: Two-grid algorithms for the Navier-Stokes equations, Numer. Math., 68 (1994), pp. 189-213.
2. H. BRÉZIS AND T. GALLOUET, Nonlinear Schrödinger evolution equations, Nonlinear Anal., 4 (1980), pp. 677-681.
3. J. R. CANNON, R. E. EWING, Y. N. HE, AND Y. P. LIN, A modified nonlinear Galerkin method for the viscoelastic fluid motion equations, Internat. J. Engrg. Sci., 37 (1999), pp. 1643-1662.
4. C. CANUTO, M. Y. HUSSAINI, A. QUARTERONI, AND T. A. ZANG, Spectral Methods in Fluid Dynamics, Springer-Verlag, New York, Heidelberg, Berlin, 1987.
5. C. DEVULDER AND M. MARION, A class of numerical algorithms for large time integration: The nonlinear Galerkin methods, SIAM J. Numer. Anal., 29 (1992), pp. 462-483.
6. C. DEVULDER, M. MARION, AND E. S. TITI, On the rate of convergence of nonlinear Galerkin methods, Math. Comp., 60 (1993), pp. 495-514.
7. C. FOIAS, O. MANLEY, AND R. TEMAM, Modeling of the interaction of small and large eddies in two-dimensional turbulent flow, Math. Model. Numer. Anal., 22 (1988), pp. 93-114.
8. B. GARCIA-ARCHILLA, J. Novo, AND E. S. TITI, An approximate inertial manifolds approach to postprocessing the Galerkin method for the Navier-Stokes equations, Math. Comp., 68 (1999), pp. 893-911.
9. Y. HE AND K. Li, Convergence and stability a ffinite element nonlinear Galerkin method for the Navier-Stokes equations, Numer. Math., 79 (1998), pp. 77-106.
10. Y. HE AND K. Li, Taylor expansion algorithm for the nonlinear operator equations, Acta Math. Sinica, 41 (1998), pp. 317-326.
11. Y. HE, Y. Hou, AND K. Li, Stability and convergence of optimum spectral non-linear Galerkin methods, Math. Methods Appl. Sci., 24 (2001), pp. 298-317.
12. J. G. HEYWOOD AND R. RANNACHER, On the question of turbulence modeling by approximate inertial manifolds and the nonlinear Galerkin method, SIAM J. Numer. Anal., 30 (1993), pp. 1603-1621.
13. K. Li AND Y. Hou, An AIM and one step Newton method for the Navier-Stokes equations, Comput. Methods Appl. Mech. Engrg., 190 (2001), pp. 6141-6155.
14. K. Li AND Y. Hou, Fourier nonlinear Galerkin method for N-S equations, Discrete Contin. Dynam. Systems, 2 (1996), pp. 497-524.
15. M. MARION AND R. TEMAM, Nonlinear Galerkin methods, SIAM J. Numer. Anal., 26 (1989), pp. 1139-1157.
16. M. MARION AND R. TEMAM, Nonlinear Galerkin methods: The finite element case, Numer. Math., 57 (1990), pp. 205-226.
17. M. MARION AND J. Xu, Error estimates on a new nonlinear Galerkin method based on two-grid finite elements, SIAM J. Numer. Anal., 32 (1995), pp. 1170-1184.
18. J. SHEN, Long time stability and convergence for fully discrete nonlinear Galerkin methods, Appl. Anal, 38 (1990), pp. 201-229.
19. J. SHEN AND R. TEMAM, Nonlinear Galerkin method using Chebyshev and Legendre polynomials I. The one-dimensional case, SIAM J. Numer. Anal., 32 (1995), pp. 215-234.
20. R. TEMAM, Stability analysis of the nonlinear Galerkin method, Math. Comp., 57 (1991), pp. 477-505.
21. R. TEMAM, Navier-Stokes Equations, Theory and Numerical Analysis, 3rd ed., North-Holland, Amsterdam, 1984.
22. R. TEMAM, Infinite-Dimensional Dynamical Systems in Mechanics and Physics, Springer-Verlag, New York, 1988.