Navier－Stokes方程的非线性Galerkin方法和Crank－Nicolson逼近

NONLINEAR GALERKIN METHOD AND CRAND-NICOLSON APPROXIMATION FOR THE NAVIER STOKES EQUATIONS

研究二维非定常的Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程的初边值问题，并且给出了数值求解Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程的一种新的全离散化格式，这种格式在于将空间变量离散的非线性Ｇａｌｅｒｋｉｎ有限元方法和时间变量离散的Ｃｒａｎｋ－Ｎｉｃｏｌｓｏｎ逼近结合起来，此外，对应于这种格式的逼近解的收敛精度给予了证明。

This paper studies the initial-boundary value problem of 2-D nonstationary Navier-Stokes equations and gives a new full discrete numerical scheme,which consists in combiningthe nonlinear Galerkin finite element method with the Crank-Nicolson approximation,More-over,this paper provides the convergence accuracy of the numerical solution correspondingto this scheme.