A comparative study of least-squares, SUPG and Galerkin methods for convection problems

International Journal of Computational Fluid Dynamics

Volumn 15, Issue 2, 2001, Pages 127-146

  Bochev, Pavel B ^a   Choi, Jungmin ^a  

^a UNIVERSITY OF TEXAS AT ARLINGTON   (United States)

Author keywords

Convection problems; Finite element methods; Galerkin methods; Least squares; Streamline upwinding; SUPG

Indexed keywords

EID: 23044528817     PISSN: 10618562     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Review

References (18)

1. Almeida, R. C. and Silva, R. S. (1997). A stable Petrov-Galerkin method for convection-dominated problems, Comput. Meth. Appl. Mech. Engrg., 140, 291-304.
2. Bochev, P. and Gunzburger, M. D. (1998). Finite element methods of least-squares type SIAM Review, 40(4), 789-837.
3. Carey, G. F. and Jiang, B. N. (1988). Least-squares finite elements for first-order hyperbolic systems, Int. J. Num. Meth. Engng., 26, 81-93.
4. Carey, G. F., Jiang, B. N. and Showalter, R. (1988). A regularization-stabilization technique for nonlinear conservation equations computations, Num. Meth. PDE's, 4, 165-171.
5. Chen, T. F. (1992). Semidiscrete least-squares methods for linear hyperbolic systems, Numerical Methods for Partial Differential Equations, 8, 423-442.
6. Deconinck, H., Powell, K., Roe, P. and Struijs, R., AIAA-91-1532-CP.
7. Do Carmo, E. G. and Galeao, A. (1991). Feedback Petrov-Galerkin methods for convection-dominated problems, Comput. Meth. Appl. Mech. Engrg., 88, 1-16.
8. Do Carmo, E. G. and Galeao, A. (1988). A consistent upwind Petrov-Galerkin method for convection-dominated problems, Comput. Meth. Appl. Mech. Engrg., 68, 83-95.
9. Eriksson, K., Estep, D., Hansbo, P. and Johnson, C., Computational Differential Equations, Cambridge University Press, 1996.
10. Fiard, J. M., Manteuffel, T. A. and McCormick, S. F., First-order system least-squares (FOSLS) for convection-diffusion problems: numerical results, submitted.
11. Fix, G. J. and Stephan, E., Finite Element Methods of Least-Squares Type for Regions with Corners, ICASE Report No. 81-41, NASA Langley Research Center, Hampton, VA 23665, 1981.
12. Jiang, B. N. and Carey, G. F. (1988). A stable least-squares finite element method for nonlinear hyperbolic problems, Int. J. Num. Meth. Fluids, 8, 933-942.
13. Jiang, B. N. (1993). Non-oscillatory and non-diffusive solution of convection problems by the iteratively reweighted least-squares finite element method, J. Comp. Phys., 105(1), 108-121.
14. Hughes, T. J. R. and Brooks, A. (1982). A theoretical framework for Petrov-Galerkin methods with discontinuous weighting functions: Application to the streamline-upwind procedure, Finite Elements in Fluids, 4, Edited by Gallagher, R. H. et al., J. Willey and Sons, 47-65.
15. Hughes, T. J. R., Mallet, M. and Mizukami, A. (1986). A new finite element formulation for computational fluid dynamics: II. Beyond SUPG, Comput. Meth. Appl. Mech. Engrg., 54, 341-355.
16. Johnson, C., Navert, U. and Pitkaranta, J. (1984). Finite element methods for linear hyperbolic problems, Comput. Meth. Appl. Mech. Engrg., 45, 285-312.
17. Lazarov, R. D., Tobiska, L. and Vassilevski, P. S. (1997). Streamline-diffusion least-squares mixed finite element methods for convection-diffusion problems, East-west J. Numer. Math, 5(4), 249-264.
18. Miller, K. and Baines, M., Least-squares moving finite elements, Report No. 98/06, Oxford University Computing Laboratory, Numerical Analysis Group, 1998.