对流-扩散问题的Galerkin部分迎风有限元方法

时(其中h表示典型的网格尺寸),将会出现数值解的伪振荡.为了克服这种数值不稳定性,人们提出了多种解决途径,例如采用迎风型的差分格式.Zienkiewicz等人首先提出用Petrov-Galerkin有限元法求解对流-扩散问题.他们通过分别选择解空间和检验函数空间,克服了数值不稳定性.但这类方法由于解空间和检验函数空间的基函数比较

GALERKIN PARTIAL UPWIND FINITE ELEMENT METHOD FOR THE CONVECTION-DIFFUSION EQUATIONS

This paper deals with a kind of Galerkin finite element method called partial upwindfinite element for steady convection-diffusion problem. With suitable local upwind coefficientsthe finite element solution satisfies discrete maximun principle and the superfluous amountof additional viscosity can be reduced in order to reproduce the shape of the exact solutionas sharply as possible. For one-dimensional case this method leads to the well-known ll'in'sscheme.