SOME UPWINDING TECHNIQUES FOR FINITE-ELEMENT APPROXIMATIONS OF CONVECTION-DIFFUSION EQUATIONS

被引:60
作者
BANK, RE
BURGLER, JF
FICHTNER, W
SMITH, RK
机构
[1] SWISS FED INST TECHNOL, INTEGRATED SYST LAB, CH-8092 ZURICH, SWITZERLAND
[2] AT&T BELL LABS, MURRAY HILL, NJ 07974 USA
关键词
Subject classifications: AMS(MOS); 65N05; 65N10; 65N20; CR:; G1.8;
D O I
10.1007/BF01385618
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
A uniform framework for the study of upwinding schemes is developed. The standard finite element Galerkin discretization is chosen as the reference discretization, and differences between other discretization schemes and the reference are written as artificial diffusion terms. These artificial diffusion terms are spanned by a four dimensional space of element diffusion matrices. Three basis matrices are symmetric, rank one diffusion operators associated with the edges of the triangle; the fourth basis matrix is skew symmetric and is associated with a rotation by φ{symbol}/2. While finite volume discretizations may be written as upwinded Galerkin methods, the converse does not appear to be true. Our approach is used to examine several upwinding schemes, including the streamline diffusion method, the box method, the Scharfetter-Gummel discretization, and a divergence-free scheme. © 1990 Springer-Verlag.
引用
收藏
页码:185 / 202
页数:18
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