Comparison of some finite element methods for solving the diffusion-convection-reaction equation

被引:356
作者
Codina, R [1 ]
机构
[1] Univ Politecn Catalunya, Escola Tecn Super Engn Camins Canals & Ports, ES-08034 Barcelona, Spain
关键词
D O I
10.1016/S0045-7825(97)00206-5
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
In this paper we describe several finite element methods for solving the diffusion-convection-reaction equation. None of them is new, although the presentation is non-standard in an effort to emphasize the similarities and differences between them. In particular, it is shown that the classical SUPG method is very similar to an explicit version of the Characteristic-Galerkin method, whereas the Taylor-Galerkin method has a stabilization effect similar to a sub-grid scale model, which is in turn related to the introduction of bubble functions. (C) 1998 Elsevier Science S.A.
引用
收藏
页码:185 / 210
页数:26
相关论文
共 36 条
[21]  
Hughes T.J.R., 1982, FINITE ELEMENTS FLUI, V4, P46
[23]   A NEW FINITE-ELEMENT FORMULATION FOR COMPUTATIONAL FLUID-DYNAMICS .8. THE GALERKIN LEAST-SQUARES METHOD FOR ADVECTIVE-DIFFUSIVE EQUATIONS [J].
HUGHES, TJR ;
FRANCA, LP ;
HULBERT, GM .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1989, 73 (02) :173-189
[24]   A NEW FINITE-ELEMENT FORMULATION FOR COMPUTATIONAL FLUID-DYNAMICS .5. CIRCUMVENTING THE BABUSKA-BREZZI CONDITION - A STABLE PETROV-GALERKIN FORMULATION OF THE STOKES PROBLEM ACCOMMODATING EQUAL-ORDER INTERPOLATIONS [J].
HUGHES, TJR ;
FRANCA, LP ;
BALESTRA, M .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1986, 59 (01) :85-99
[25]   MULTISCALE PHENOMENA - GREENS-FUNCTIONS, THE DIRICHLET-TO-NEUMANN FORMULATION, SUBGRID SCALE MODELS, BUBBLES AND THE ORIGINS OF STABILIZED METHODS [J].
HUGHES, TJR .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1995, 127 (1-4) :387-401
[27]  
HUGHES TJR, 1979, FEM CONVECTION DOMIN
[28]   FINITE-ELEMENT METHODS FOR LINEAR HYPERBOLIC PROBLEMS [J].
JOHNSON, C ;
NAVERT, U ;
PITKARANTA, J .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1984, 45 (1-3) :285-312
[29]   A NOTE ON UPWINDING AND ANISOTROPIC BALANCING DISSIPATION IN FINITE-ELEMENT APPROXIMATIONS TO CONVECTIVE DIFFUSION-PROBLEMS [J].
KELLY, DW ;
NAKAZAWA, S ;
ZIENKIEWICZ, OC ;
HEINRICH, JC .
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 1980, 15 (11) :1705-1711
[30]  
LeVeque R.J., 1990, Numerical Methods For Conservation Laws