A multiscale/stabilized finite element method for the advection-diffusion equation

Computer Methods in Applied Mechanics and Engineering

Volumn 193, Issue 21-22, 2004, Pages 1997-2018

  Masud, A ^a   Khurram, R A ^a  

^a UNIVERSITY OF ILLINOIS AT CHICAGO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; DECOMPOSITION; FINITE ELEMENT METHOD; GALERKIN METHODS; PARAMETER ESTIMATION;

ADVECTION-DIFFUSION EQUATIONS; SCALAR FIELDS;

DIFFUSION;

ADVECTION-DIFFUSION EQUATION; COMPUTER APPLICATION; FINITE ELEMENT METHOD;

EID: 1842636700     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2003.12.047     Document Type: Article

References (22)

1. Baiocchi C. Bezzi F. Franca L.P. Virtual bubbles and Galerkin-least-squares type methods (Ga.L.S) Comput. Methods Appl. Mech. Engrg. 105 1993 125-141
2. Brezzi F. Bristeau M.O. Franca L.P. Mallet M. Roge G. A relationship between stabilized finite element methods and the Galerkin method with bubble functions Comput. Methods Appl. Mech. Engrg. 96 1 1992 117-129
3. Brezzi F. Franca L.P. Hughes T.J.R. Russo A. b=∫g Comput. Methods Appl. Mech. Engrg. 145 3-4 1997 329-339
4. Brezzi F. Franca L.P. Russo A. Further considerations on residual-free bubbles for advective-diffusive equations Comput. Methods Appl. Mech. Engrg. 166 1-2 1998 25-33
5. Brezzi F. Houston P. Marini D. Suli E. Modeling subgrid viscosity for advection-diffusion problems Comput. Methods Appl. Mech. Engrg. 190 2000 1601-1610
6. Brezzi F. Marini D. Russo A. Application of the pseudo residual-free bubbles to the stabilization of convection-diffusion problems Comput. Methods Appl. Mech. Engrg. 166 1998 51-63
7. Brooks A.N. Hughes T.J.R. Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations Comput. Methods Appl. Mech. Engrg. 32 1-3 1982 199-259
8. Franca L.P. Farhat C. Bubble functions prompt unusual stabilized finite element methods Comput. Methods Appl. Mech. Engrg. 123 1-4 1995 299-308
9. Franca L.P. Farhat C. Lesoinne M. Russo A. Unusual stabilized finite element methods and residual free bubbles Int. J. Numer. Methods Fluids 27 2 1998 159-168
10. Franca L.P. Frey S.L. Hughes T.J.R. Stabilized finite element methods: I. Application to the advective-diffusive model Comput. Methods Appl. Mech. Engrg. 95 2 1992 253-276
11. Franca L.P. Nesliturk A. Stynes M. On the stability of residual-free bubbles for convection-diffusion problems and their approximation by a two-level finite element method Comput. Methods Appl. Mech. Engrg. 166 1-2 1998 35-49
12. Franca L.P. Valentin F. On an improved unusual stabilized finite element method for the advective-reactive-diffusive equation Comput. Methods Appl. Mech. Engrg. 190 2000 1785-1800
13. Harari I. Franca L.P. Oliveira S.P. Streamline design of stability parameters for advection-diffusion problems J. Comput. Phys. 171 1 2001 115-131
14. Hughes T.J.R. Multiscale phenomena: Green's functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized methods Comput. Methods Appl. Mech. Engrg. 127 1995 387-401
15. Hughes T.J.R. The Finite Element Method: Linear Static and Dynamic Finite Element Analysis 1987 Prentice-Hall Englewoods Cliffs, NJ Dover edition, 2000
16. T.J.R. Hughes, A.N. Brooks, Streamline-upwind/Petrov-Galerkin methods for advection dominated flows, in: Proceedings of the Third International Conference on Finite Element Methods in Fluid Flow, Banff, June 1980, pp. 283-292
17. Hughes T.J.R. Feijoo G.R. Luca M. Jean-Baptiste Q. The variational multiscale method--a paradigm for computational mechanics Comput. Methods Appl. Mech. Engrg. 166 1-2 1998 3-24
18. Hughes T.J.R. Franca L.P. Hulbert G.M. A new finite element formulation for computational fluid dynamics: VIII. The Galerkin/least-squares method for advective-diffusive equations Comput. Methods Appl. Mech. Engrg. 73 2 1989 173-189
19. Masud A. Hughes T.J.R. A stabilized mixed finite element method for Darcy flow Comput. Methods Appl. Mech. Engrg. 191/39-40 2002 4341-4370
20. A. Masud, On a stabilized finite element formulation for incompressible Navier-Stokes equations, in: Proceedings of the Fourth US-Japan Conference on Computational Fluid Dynamics, Tokyo, Japan, May 28-30, 2002
21. Ayub M. Masud A. A new stabilized formulation for convective-diffusive heat transfer Numer. Heat Transfer Part B 44 2003 1-23
22. Tezduyar T.E. Park Y.J. Discontinuity-capturing finite element formulations for nonlinear convection-diffusion-reaction equations Comput. Methods Appl. Mech. Engrg. 59 1986 307-325