On the choice of a stabilizing subgrid for convection-diffusion problems

被引:39
作者
Brezzi, F
Marini, LD
Russo, A
机构
[1] Univ Pavia, Dipartimento Matemat, I-27100 Pavia, Italy
[2] CNR, IMATI, I-27100 Pavia, Italy
[3] Univ Milano Bicocca, Dipartimento Matemat & Applicaz, Milan, Italy
关键词
finite elements; advection-diffusion; stabilizations; augmented grids;
D O I
10.1016/j.cma.2004.02.022
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
SUPG and residual-free bubbles are closely related methods that have been used with success to stabilize a certain number of problems, including advection-dominated flows. In recent times, a slightly different idea has been proposed: to choose a suitable subgrid in each element, and then solving Standard Galerkin on the Augmented Grid. For this, however, the correct location of the subgrid node(s) plays a crucial role. Here, for the model problem of linear advection-diffusion equations, we propose a simple criterion to choose a single internal node such that the corresponding plain-Galerkin scheme on the augmented grid provides the same a priori error estimates that are typically obtained with SUPG or RFB methods. (C) 2004 Elsevier B.V. All rights reserved.
引用
收藏
页码:127 / 148
页数:22
相关论文
共 27 条
[1]   VIRTUAL BUBBLES AND GALERKIN-LEAST-SQUARES TYPE METHODS (GA.L.S.) [J].
BAIOCCHI, C ;
BREZZI, F ;
FRANCA, LP .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1993, 105 (01) :125-141
[2]   A RELATIONSHIP BETWEEN STABILIZED FINITE-ELEMENT METHODS AND THE GALERKIN METHOD WITH BUBBLE FUNCTIONS [J].
BREZZI, F ;
BRISTEAU, MO ;
FRANCA, LP ;
MALLET, M ;
ROGE, G .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1992, 96 (01) :117-129
[3]   A priori error analysis of residual-free bubbles for advection-diffusion problems [J].
Brezzi, F ;
Hughes, TJR ;
Marini, LD ;
Russo, A ;
Süli, E .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1999, 36 (06) :1933-1948
[4]   CHOOSING BUBBLES FOR ADVECTION-DIFFUSION PROBLEMS [J].
BREZZI, F ;
RUSSO, A .
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 1994, 4 (04) :571-587
[5]  
Brezzi F, 2000, NUMER MATH, V85, P31, DOI 10.1007/s002110000128
[6]   Link-cutting bubbles for the stabilization of convection-diffusion-reaction problems [J].
Brezzi, F ;
Hauke, G ;
Marini, LD ;
Sangalli, G .
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2003, 13 (03) :445-461
[7]   Augmented spaces, two-level methods, and stabilizing subgrids [J].
Brezzi, F ;
Marini, LD .
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, 2002, 40 (1-2) :31-46
[8]   Applications of the pseudo residual-free bubbles to the stabilization of convection-diffusion problems [J].
Brezzi, F ;
Marini, D ;
Russo, A .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1998, 166 (1-2) :51-63
[9]   Modeling subgrid viscosity for advection-diffusion problems [J].
Brezzi, F ;
Houston, P ;
Marini, D ;
Süli, E .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2000, 190 (13-14) :1601-1610
[10]  
BREZZI F, 2002, SPRINGER LECT NOTES, V19, P73