A C^0-WEAK GALERKIN FINITE ELEMENT METHOD FOR THE TWO-DIMENSIONAL NAVIER-STOKES EQUATIONS IN STREAM-FUNCTION FORMULATION  

作　　者：Baiju Zhang Yan Yang Minfu Feng 

机构地区：[1]School of Mathematics,Sichuan University,Chengdu 610064,China [2]School of Sciences,Southwest Petroleum University,Chengdu 610500,China

出　　处：《Journal of Computational Mathematics》2020年第2期310-336,共27页计算数学（英文）

基　　金：the National Natural Science Foundation of China(No.11271273).

摘　　要：We propose and analyze a C^0-weak Galerkin(WG)finite element method for the numerical solution of the Navier-Stokes equations governing 2D stationary incompressible flows.Using a st ream-function formulation,the system of Navier-Stokes equations is reduced to a single fourth-order nonlinear partial differential equation and the incompressibility constraint is automatically satisfied.The proposed method uses continuous piecewisepolynomial approximations of degree k+2 for the stream-function 0 and discontinuous piecewise-polynomial approximations of degreek+1 for the trace of V-0 on the interelement boundaries.The existence of a discrete solution is proved by means of a topological degree argument,while the uniqueness is obtained under a data smallness condition.An optimal error estimate is obtained in L^2-norm,H^1-norm and brokenH^2-norm.Numerical tests are presented to demonstrate the theoretical results.

关 键 词：Weak Galerkin method Navier-S to kes equations St ream-function formulation. 

分 类 号：O241.82[理学—计算数学]