Some observations on generalized saddle-point problems

SIAM Journal on Matrix Analysis and Applications

Volumn 25, Issue 1, 2004, Pages 224-236

  Ciarlet Jr , P ^a   Huang, Jianguo ^b   Zou, Jun ^c  

^a ENSTA PARISTECH   (France)

^b SHANGHAI JIAO TONG UNIVERSITY   (China)

^c CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Generalized saddle point problems; Solvability; Stability

Indexed keywords

EID: 1342267538     PISSN: 08954798     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0895479802410827     Document Type: Article

References (14)

1. I. BABUSKA AND A. AZIZ, Survey lectures on the mathematical foundations of the finite element method, in The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations, A. Aziz, ed., Academic Press, New York, 1973, pp. 1-359.
2. C. BERNARDI, C. CANUTO, AND Y. MADAY, Generalized inf-sup conditions for Chebyshev spectral approximation of the Stokes problem, SIAM J. Numer. Anal., 25 (1988), pp. 1237-1271.
3. F. BREZZI, On the existence, uniqueness and approximation of saddle point problems arising from Lagrange multipliers, RAIRO Math. Model. Numer. Anal., 8 (1974), pp. 129-151.
4. F. BREZZI AND M. FORTIN, Mixed and Hybrid Element Methods, Springer-Verlag, New York, 1991.
5. P. CIARLET, JR. AND J. Zou, Finite element convergence for the Darwin model to Maxwell's equations, RAIRO Math. Model. Numer. Anal., 31 (1997), pp. 213-250.
6. J. DOUGLAS, JR. AND J. ROBERTS, Global estimates for mixed methods for second order elliptic equations, Math. Comput., 44 (1985), pp. 39-52.
7. V. GIRAULT AND P. RAVIART, Finite Element Methods for Navier-Stokes Equations, Springer-Verlag, New York, 1986.
8. G. H. GOLUB AND C. F. VAN LOAN, Matrix Computation, 2nd ed., Johns Hopkins University Press, Baltimore, 1989.
9. Q. HU AND J. ZOU, An iterative method with variable relaxation parameters for saddle-point problems, SIAM J. Matrix Anal. Appl., 23 (2001), pp. 317-338.
10. Q. Hu AND J. ZOU, Two new variants of nonlinear inexact Uzawa algorithms for saddle-point problems, Numer. Math., 93 (2002), pp. 333-359.
11. R. B. KELLOGG AND B. LIU, A finite element method for compressible Stokes equations, SIAM J. Numer. Anal., 33 (1996), pp. 780-788.
12. R. MACCAMY, Variational procedures for a class of exterior interface problems, J. Math. Anal. Appl., 78 (1980), pp. 248-266.
13. R. A. NICOLAIDES, Existence, uniqueness and approximation for generalized saddle point problems, SIAM J. Numer. Anal., 19 (1982), pp. 349-357.
14. D. YANG, Iterative schemes for mixed finite element methods with applications to elasticity and compressible flow problems, Numer. Math., 93 (2002), pp. 177-200.