The nearly-optimal Petrov-Galerkin method for convection-diffusion problems

Computer Methods in Applied Mechanics and Engineering

Volumn 192, Issue 22-23, 2003, Pages 2501-2519

  Nesliturk, Ali ^a   Harari, Isaac ^b  

^a IZMIR INSTITUTE OF TECHNOLOGY   (Turkey)

^b TEL AVIV UNIVERSITY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

COERCIVE FORCE; CONVERGENCE OF NUMERICAL METHODS; DIFFUSION; ERROR ANALYSIS; FINITE ELEMENT METHOD;

CONVECTION-DIFFUSION;

TRANSPORT PROPERTIES;

CONVECTION-DIFFUSION EQUATION; FINITE ELEMENT METHOD; SOLUTE TRANSPORT;

EID: 0038685656     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7825(03)00269-X     Document Type: Article

References (17)

1. Babuška I. Melenk J.M. The partition of unity method Int. J. Numer. Methods Engrg. 40 4 1997 727-758
2. 1-optimal finite element methods Comput. Methods Appl. Mech. Engrg. 190 43-44 2001 5679-5690
3. Brenner S. Scott L. The Mathematical Theory of Finite Element Methods 1994 Springer-Verlag New York
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. 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
6. Farhat C. Harari I. Franca L.P. The discontinuous enrichment method Comput. Methods Appl. Mech. Engrg. 190 48 2001 6455-6479
7. Franca L.P. Prey 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
8. Franca L.P. Nesliturk A. On a two-level finite element method for the incompressible Navier-Stokes equations Int. J. Numer. Methods Engrg. 52 2001 433-453
9. 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
10. 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
11. 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 1-4 1995 387-401
12. Hughes T.J.R. Brooks A.N. A multidimensional upwind scheme with no crosswind diffusion Hughes T.J.R. Finite Element Methods For Convection Dominated Flows AMD vol. 34 1979 19-35 ASME New York
13. 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
14. Melenk J.M. Babuška I. The partition of unity method finite element method: basic theory and applications Comput. Methods Appl. Mech. Engrg. 139 1-4 1996 289-314
15. Oberai A.A. Pinsky P.M. A multiscale finite element method for the Helmholtz equation Comput. Methods Appl. Mech. Engrg. 154 3-4 1998 281-297
16. Protter M.H. Weinberger H.F. Maximum Principles in Differential Equations 1967 Prentice-Hall New Jersey
17. Strouboulis T. Babuška I. Copps K. The design and analysis of the generalized finite element method Comput. Methods Appl. Mech. Engrg. 181 1-3 2000 43-69