메뉴 건너뛰기




Volumn 41, Issue 2, 2003, Pages 695-714

The postprocessing Galerkin and nonlinear Galerkin methods - A truncation analysis point of view

Author keywords

Approximate inertial manifolds; Dissipative equations; Multigrid; Nonlinear Galerkin methods; Postprocessing algorithm; Spectral methods

Indexed keywords

APPROXIMATE INERTIAL MANIFOLDS; DISSIPATIVE EQUATIONS; MULTIGRID; NONLINEAR GALERKIN METHODS; POSTPROCESSING ALGORITHMS; SPECTRAL METHODS;

EID: 2342567055     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142901390500     Document Type: Article
Times cited : (39)

References (24)
  • 3
    • 0026846243 scopus 로고
    • A class of numerical algorithms for large time integration: The nonlinear Galerkin methods
    • 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.
    • (1992) SIAM J. Numer. Anal. , vol.29 , pp. 462-483
    • Devulder, C.1    Marion, M.2
  • 4
    • 84968484137 scopus 로고
    • On the rate of convergence of the nonlinear Galerkin methods
    • C. DEVULDER. M. MARION, AND E. S. TITI, On the rate of convergence of the nonlinear Galerkin methods, Math. Comp., 60 (1993) pp. 495-514.
    • (1993) Math. Comp. , vol.60 , pp. 495-514
    • Devulder, C.1    Marion, M.2    Titi, E.S.3
  • 5
    • 0000640737 scopus 로고
    • Modelling of the interaction of small and large eddies in two dimensional turbulent flow
    • C. FOIAS, O. MANLEY, AND R. TEMAM, Modelling of the interaction of small and large eddies in two dimensional turbulent flow, RAIRO Modél. Math. Anal. Numér., 22 (1988), pp. 93-118.
    • (1988) RAIRO Modél. Math. Anal. Numér. , vol.22 , pp. 93-118
    • Foias, C.1    Manley, O.2    Temam, R.3
  • 6
    • 0000640733 scopus 로고
    • Inertial manifolds for nonlinear evolutionary equations
    • C. FOIAS, G. SELL. AND R. TEMAM, Inertial manifolds for nonlinear evolutionary equations, J. Differential Equations, 73 (1988), pp. 309-353.
    • (1988) J. Differential Equations , vol.73 , pp. 309-353
    • Foias, C.1    Sell, G.2    Temam, R.3
  • 7
    • 0001686992 scopus 로고
    • Exponential tracking and approximation of inertial manifolds for dissipative nonlinear equations
    • C. FOIAS, G. SELL, AND E. S. TITI, Exponential tracking and approximation of inertial manifolds for dissipative nonlinear equations, J. Dynam. Differential Equations, 1 (1989), pp. 199-244.
    • (1989) J. Dynam. Differential Equations , vol.1 , pp. 199-244
    • Foias, C.1    Sell, G.2    Titi, E.S.3
  • 8
    • 0039011694 scopus 로고    scopus 로고
    • A postprocessed Galerkin method with Chebyshev and Legendre polynomials
    • J. DE FRUTOS, B. GARCÍA-ARCHILLA, AND J. NOVO, A postprocessed Galerkin method with Chebyshev and Legendre polynomials, Numer. Math., 86 (2000), pp. 377-417.
    • (2000) Numer. Math. , vol.86 , pp. 377-417
    • De Frutos, J.1    García-Archilla, B.2    Novo, J.3
  • 9
    • 0001946354 scopus 로고
    • Some practical experience with the time integration of dissipative equations
    • B. GARCÍA-ARCHILLA, Some practical experience with the time integration of dissipative equations, J. Comput. Phys., 122 (1995), pp. 25-29.
    • (1995) J. Comput. Phys. , vol.122 , pp. 25-29
    • García-Archilla, B.1
  • 10
    • 0001324638 scopus 로고    scopus 로고
    • Postprocessing the Galerkin method: A novel approach to approximate inertial manifolds
    • B. GARCIÁ-ARCHILLA, J. NOVO, AND E. S. TITI, Postprocessing the Galerkin method: A novel approach to approximate inertial manifolds, SIAM J. Numer. Anal., 35 (1998), pp. 941-972.
    • (1998) SIAM J. Numer. Anal. , vol.35 , pp. 941-972
    • Garciá-Archilla, B.1    Novo, J.2    Titi, E.S.3
  • 11
    • 0038855060 scopus 로고    scopus 로고
    • An approximate inertial manifolds approach to postprocessing the Galerkin method for the Navier-Stokes equations
    • B. GARCIÁ-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.
    • (1999) Math. Comp. , vol.68 , pp. 893-911
    • Garciá-Archilla, B.1    Novo, J.2    Titi, E.S.3
  • 12
    • 0000051734 scopus 로고    scopus 로고
    • Postprocessing the Galerkin method: The finite-element case
    • B. GARCÍA-ARCHILLA AND E. S. TITI, Postprocessing the Galerkin method: The finite-element case, SIAM J. Numer. Anal., 37 (2000), pp. 470-499.
    • (2000) SIAM J. Numer. Anal. , vol.37 , pp. 470-499
    • García-Archilla, B.1    Titi, E.S.2
  • 13
    • 34047228827 scopus 로고
    • Approximate inertial manifolds for the Kuramoto-Sivashinsky equation: Analysis and computations
    • M. S. JOLLY, I. G. KEVREKIDIS, AND E. S. TITI, Approximate inertial manifolds for the Kuramoto-Sivashinsky equation: Analysis and computations, Phys. D, 44 (1990), pp. 38-60.
    • (1990) Phys. D , vol.44 , pp. 38-60
    • Jolly, M.S.1    Kevrekidis, I.G.2    Titi, E.S.3
  • 14
    • 0001630939 scopus 로고
    • Preserving dissipation in approximate inertial forms for the Kuramoto-Sivashinsky equation
    • M. S. JOLLY, I. G. KEVREKIDIS, AND E. S. TITI, Preserving dissipation in approximate inertial forms for the Kuramoto-Sivashinsky equation, J. Dynam. Differential Equations, 3 (1991), pp. 179-197.
    • (1991) J. Dynam. Differential Equations , vol.3 , pp. 179-197
    • Jolly, M.S.1    Kevrekidis, I.G.2    Titi, E.S.3
  • 15
    • 0040678264 scopus 로고
    • A Remark on quasi-stationary approximate inertial manifolds for the D Navier-Stokes equations
    • D. A. JONES AND E. S. TITI, A Remark on quasi-stationary approximate inertial manifolds for the D Navier-Stokes equations, SIAM J. Math. Anal., 25 (1994), pp. 894-914.
    • (1994) SIAM J. Math. Anal. , vol.25 , pp. 894-914
    • Jones, D.A.1    Titi, E.S.2
  • 16
    • 0000547750 scopus 로고
    • Nonlinear Galerkin methods
    • M. MARION AND R. TEMAM, Nonlinear Galerkin methods, SIAM J. Numer. Anal., 26 (1989), pp. 1139-1157.
    • (1989) SIAM J. Numer. Anal. , vol.26 , pp. 1139-1157
    • Marion, M.1    Temam, R.2
  • 17
    • 0035593250 scopus 로고    scopus 로고
    • Efficient methods using high accuracy approximate inertial manifolds
    • J. NOVO, E. S. TITI, AND S. WYNNE, Efficient methods using high accuracy approximate inertial manifolds, Numer. Math., 87 (2001), pp. 555-595.
    • (2001) Numer. Math. , vol.87 , pp. 555-595
    • Novo, J.1    Titi, E.S.2    Wynne, S.3
  • 18
    • 0003278399 scopus 로고
    • Infinite-dimensional dynamical systems in mechanics and physics
    • Springer-Verlag, New York
    • R. TEMAM, Infinite-Dimensional Dynamical Systems in Mechanics and Physics, Appl. Math. Sci. 68, Springer-Verlag, New York, 1988.
    • (1988) Appl. Math. Sci. , vol.68
    • Temam, R.1
  • 19
    • 0011603756 scopus 로고
    • Attractors for the Navier-Stokes equations, localization and approximation
    • R. TEMAM, Attractors for the Navier-Stokes equations, Localization and approximation, J. Fac. Sci. Univ. Tokyo, Sect. IA Math., 36 (1989), pp. 629-647.
    • (1989) J. Fac. Sci. Univ. Tokyo, Sect. IA Math. , vol.36 , pp. 629-647
    • Temam, R.1
  • 20
    • 0000372952 scopus 로고
    • Navier-Stokes equations and nonlinear functional analysis, 2nd ed.
    • SIAM, Philadelphia
    • R. TEMAM, Navier-Stokes Equations and Nonlinear Functional Analysis, 2nd ed. CBMS-NSF Regional Conf. Ser. in Appl. Math. 66, SIAM, Philadelphia, 1995.
    • (1995) CBMS-NSF Regional Conf. Ser. in Appl. Math. , vol.66
    • Temam, R.1
  • 21
    • 0025450096 scopus 로고
    • On approximate inertial manifolds to the Navier-Stokes equations
    • E. S. TITI, On approximate inertial manifolds to the Navier-Stokes equations, J. Math. Anal. Appl., 149 (1990), pp. 540-557.
    • (1990) J. Math. Anal. Appl. , vol.149 , pp. 540-557
    • Titi, E.S.1
  • 22
    • 0023420776 scopus 로고
    • On a criterion for locating stable stationary solutions to the Navier-Stokes equations
    • E. S. TITI, On a criterion for locating stable stationary solutions to the Navier-Stokes equations, Nonlinear Anal., 9 (1987), pp. 1085-1102.
    • (1987) Nonlinear Anal. , vol.9 , pp. 1085-1102
    • Titi, E.S.1
  • 24
    • 0034369956 scopus 로고    scopus 로고
    • Stability and convergence for the reform postprocessing Galerkin method
    • HE YINNIAN AND R. M. M. MATTHEIJ, Stability and convergence for the reform postprocessing Galerkin method, Nonlinear Anal. Real World Appl., 4 (2000), pp. 517-533.
    • (2000) Nonlinear Anal. Real World Appl. , vol.4 , pp. 517-533
    • Yinnian, H.1    Mattheij, R.M.M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.