Fourier Nonlinear Galerkin Approximation for the Two Dimensional Navier-Stokes Equations

Hou Yanren

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Hou Yanren. Fourier Nonlinear Galerkin Approximation for the Two Dimensional Navier-Stokes Equations[J]. Applied Mathematics and Mechanics, 1996, 17(9): 829-836.

Citation:

Hou Yanren. Fourier Nonlinear Galerkin Approximation for the Two Dimensional Navier-Stokes Equations[J]. Applied Mathematics and Mechanics, 1996, 17(9): 829-836.

Citation:

Hou Yanren. Fourier Nonlinear Galerkin Approximation for the Two Dimensional Navier-Stokes Equations[J]. Applied Mathematics and Mechanics, 1996, 17(9): 829-836.

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Fourier Nonlinear Galerkin Approximation for the Two Dimensional Navier-Stokes Equations

Hou Yanren

Research Centre for Applied Mathematics, Xi'an Jiaotong Uniuersity, Xi'an 710049, P. R. China

Publish Date: 1996-09-15

Abstract

Abstract

In this paper,for viscous incompressible Navier-Stokes equations with periodic bonndary conditions,we prove the existence and uniqueness ot the solution corresponding to its Fourier nonlinear Galerkin approximation.At the same time we give its error estimates.
- Navier-Stokes equations,
- nonlinear Galerkin methods,
- Fourier methods

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References(8)

References

[1]	C.Foias.O.Manley and R.Temam,Modelization of the interaction of small and large eddies in two dimensional turbulent flows,Math.Mod.Numer.Anal.M²AN,22(1988),93-144.
[2]	M.Marion and R.Temam,Nonlinear Galerkin methods,SIAM J.Numer.Anal.,26(1989),1139-1157.
[3]	M.Marion and R.Temam,Nonlinear Galerkin methods:the finite case elements case,Numer.Math.,57(1990),205-255.
[4]	R.Temam,Navier-Stokes Equarions,North-Holland Publishing Company,3rd revised edition(1984).
[5]	R.Teman,Navier-Stokes equations and nonlinear functional analysis,CBMS-NSF Regional Conk:Ser.in Appl.Math.,Society for Industrial and Applied Mathematics.Philadelphia,PA,(1983).
[6]	E.Weinan,Convergence of Fourier methods for the Navier-Stokes equations,SIAM J.Numer.Anal.,2(1993),650-674.
[7]	J.G.Heywood and R.Rannacher,Finite element approximation of the nonstationarv Navier-Stokes problem.I.Regularity of solutions and second-order error estimates for spatial discretization,SIAM J.Numer.Anal.,19(1982).275-311.
[8]	H.Okamoto,On the semi-discrete finite element approximation for the nonstationary Navier-Stokes equation,J,Fac.Sci.,Univ.of Tokyo Sec.IA Math,29(1982).613-652.