An estimate of the Babuška-Brezzi inf-sup discrete stability constant for general linear Petrov-Galerkin finite element formulations (an estimate of the Babuška-Brezzi stability constant)

Applied Mathematics and Computation

Volumn 144, Issue 1, 2003, Pages 107-116

  Tsamasphyros, G ^a   Markolefas, S ^a  

^a NATIONAL TECHNICAL UNIVERSITY OF ATHENS   (Greece)

Author keywords

Babu ka Brezzi stability constant; Discrete inf sup condition; Finite elements; Petrov Galerkin approximations

Indexed keywords

APPROXIMATION THEORY; FINITE ELEMENT METHOD; FUNCTIONS; LINEAR EQUATIONS;

PETROV-GALERKIN APPROXIMATIONS;

GALERKIN METHODS;

EID: 0038044644     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0096-3003(02)00395-8     Document Type: Article

References (16)

1. Aziz A.K., Babuška I. The Mathematical Foundations of the Finite Element Method with Application to Partial Differential Equations. 1972;Academic Press, New York.
2. Arnold D.N., Babuška I., Osborn J. Finite element methods: principles for their selection. Comput. Meth. Appl. Mech. Eng. 45:1984;57-96.
3. Babuška I. Error-bounds for finite element method. Numer. Math. 16:1971;322-333.
4. Brezzi F., Bathe K.-J. A discourse on the stability conditions for mixed finite element formulations. Oden J.T. Reliability in Computational Mechanics. 1990;27-57 North Holland, Amsterdam.
5. Fortin M. An analysis of the convergence of mixed finite element methods. RAIRO Anal. Numér. 11:1977;341-354.
6. Fortin M. Old and new finite elements for incompressible flows. Int. J. Numer. Meth. Fluids. 1:1981;347-364.
7. Braess D. Finite Elements. 1997;Cambridge University Press, United Kingdom.
8. Brezzi F. On the existence uniqueness and approximation of saddle-point problems arising from Lagrange multipliers. RAIRO Anal. Numér. 8(R-2):1974;129-151.
9. Babuška I., Narasimhan R. The Babuška-Brezzi condition and the patch test: an example. Comput. Meth. Appl. Mech. Eng. 140:1977;183-199.
10. Babuška I., Baumann C.E., Oden J.T. A discontinuous h-p finite element method for diffusion problems: 1-D analysis. Comput. Math. Appl. 37:1999;103-122.
11. Zienkiewicz O.C., Qu S., Taylor R.L., Nakazawa S. The patch test for mixed formulations. Int. J. Numer. Meth. Eng. 23:1986;1873-1883.
12. Zienkiewicz O.C., Taylor R.L. The finite element patch test revisited. A computer test for convergence validation and error estimates. Comput. Meth. Appl. Mech. Eng. 149:1997;223-254.
13. Ciarlet P.G. The Finite Element Method for Elliptic Problems. 1978;North-Holland Publishing Company, Amsterdam.
14. Babuška I., Szabó B.A., Katz I.N. The p-version of the finite element method. SIAM J. Numer. Anal. 18:1981;515-545.
15. Schatz A.H. An observation concerning Ritz-Galerkin methods with indefinite bilinear forms. Math. Comput. 28:1974;959-962.
16. Szabó B.A., Babuška I. Finite Element Analysis. 1991;John Wiley & Sons Inc. New York.