Wu Yujiang. Remarks on Nonlinear Galerkin Method for Kuramoto-Sivashinsky Equation[J]. Applied Mathematics and Mechanics, 1997, 18(10): 937-945.
Citation: Wu Yujiang. Remarks on Nonlinear Galerkin Method for Kuramoto-Sivashinsky Equation[J]. Applied Mathematics and Mechanics, 1997, 18(10): 937-945.

Remarks on Nonlinear Galerkin Method for Kuramoto-Sivashinsky Equation

  • Received Date: 1995-10-16
  • Rev Recd Date: 1996-11-11
  • Publish Date: 1997-10-15
  • This paper is concentrated on a nonlinear Galerkin method with sm small-scale components for Kuramoto-Sivashmsky equation,in which convergence results and the analysis of error estimates are given.The conclusion shows that this choce of modes is efficient for The method modifred.
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  • [1]
    C.Foias.O.Manley and R.Temam,Modelling of the interaction of small and largeeddies in two dimensional turbulent flows,RAIRO Math.Model Numer.Anal.,22(1988),93-118.
    [2]
    C.Foias,O.Manley,R.Teman and Y.Treve,Asymptic analysis of the Navier-Stokese quations,Physica D,9(1983),157-188.
    [3]
    J.L.Lions,Quelques Methodes de Risolution des Problemes aux Limites Non Lineaires,Dunod,Paris(1969).
    [4]
    M.Marion and R.Temam,Nonlinear Galerkin methods,SIAM J.Numer.Anal.,26(1989),1139-1157.
    [5]
    B.Nicolaenko.B.Scheurer and R.Temam,Some global dynamical properties of the Kuramoto-Sivashinsky equation:nonlinear stability and attractors,Physica D,16(1985),155-183.
    [6]
    J.Shen,Long time stability and convergence for fully discrete nonlinear Galerkin methods,Appl.Anal.,38(1990),201-229.
    [7]
    R.Temam,Navier-Slokes Equations,Third edition,North-Holland,Amsterdam,NewYork(1984).
    [8]
    R.Temam,Navier-Stokes Equations and Nonlinear Functional Analysis,CBMS-NSF Regional Conference Series in Applied Mathematics,SIAM,Philadelphia(1983).
    [9]
    R.Temam,Infinite Dimensional Dynamical Systems in Mechanics and Physics,Appl.Math.Sci.68,Springer-Verlag,Berlin,New York(1988).
    [10]
    R.Temam,Varietes innertielles approximatives pourles equations de Navier-Stokesbidimensionnelles,C.R.Acad.Sci.,Ser.II,306(1988),399-402.
    [11]
    R.Temam,Induced trajectories and approximate inertial manifolds,RAIRO Math.Model.Nwner.Anal,23(1989),541-561.
    [12]
    R.Temam,Dynamical systems.turbulence and the numerical solution of the Navier Stokes equations,in:D.L.Dwoyer and R.Voigt,eds,The Proceedings of the Eleventh International Conference on Numerical Methods in Fluid Dynamics,Lecture Notes inPhysics,Springer-Verlag(1989).
    [13]
    伍偷江,关于近似惯性流形及其数值方法的研究,力学进展,24(1994).145-153.
    [14]
    Wu Yujiang,A nonlinear Galerkin method with variable modes for Kuramoto-Sivashinshy equation:analyse and computation,J.Comput.Math.(to appear).
    [15]
    Z.H.Yang,A.Mahmood and R.S.Ye.Fully discrete nonlinear Galerkin methods for Kuramoto-Sivashinsky equation and their error estimates.J.Shanghai University(EnglishEdition),1(1997).20-27.
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