The potential fluid flow problem and the convergence rate of the minimal residual method

Numerical Linear Algebra with Applications

Volumn 3, Issue 6, 1996, Pages 525-542

  Maryška, Jiří ^a   Rozložník, Miroslav ^a   Tůma, Miroslav ^a  

^a INSTITUTE OF COMPUTER SCIENCE   (Czech Republic)

Author keywords

Asymptotic convergence factor; Minimal residual method; Mixed hybrid formulation trilateral prismatic elements; Potential flow problem in porous media; Rate of convergence; Symmetric indefinite linear systems

Indexed keywords

EID: 21444451683     PISSN: 10705325     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1099-1506(199611/12)3:6<525::AID-NLA94>3.0.CO;2-X     Document Type: Article

References (16)

1. N. I. Achieser. Über einige Funktionen, welche in zwei gegebenen Intervallen am wenigsten von Null abweichen I. Teil. Bull. Acad. Sci. URSS S., 7(9), 1163-1202, 1932.
2. A. V. Aho, J. E. Hopcroft and J. D. Ullman. The Design and Analysis of Computer Algorithms. Addison-Wesley, Reading, Menlo Park, London, Amsterdam, Don Mills, Sydney, 1976.
3. E. Anderson, Z. Bai, C. Bischof, J. Demmel, J. J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, S. Ostrouchov and D. Sorensen. LAPACK User's Guide. SIAM, Philadelphia, 1992.
4. J. A. Bondy and U. S. R. Murty. Graph Theory with Applications. London, Macmillan, 1976.
5. R. Chandra. Conjugate gradient methods for partial differential equations. Ph.D. Thesis, Yale University, New Haven, 1978.
6. M. Eiermann, X. Li and R. S. Varga. On hybrid semi-iterative methods. SIAM J. Numer. Anal., 26, 152-168, 1989.
7. B. Fischer. Chebyshev polynomials for disjoint compact sets. Constr. Approx., 8, 309-329, 1992.
8. J. Stoer and R. Freund. On the solution of large indefinite systems of linear equations by conjugate gradients algorithm. In J. L. Lions and R. Glowinski, editors, Computing Methods in Applied Sciences and Engineering, 5, 35-53, 1982.
9. A. Greenbaum and L. Gurvits. Max-Min properties of matrix factor norms. SIAM J. Sci. Comput., 15, 348-358, 1993.
10. V. I. Lebedev. Iterative methods for the solution of operator equations with their spectrum lying on several intervals. J. Comput. Math. and Math. Phys., 9, 1247-1252, 1969.
11. J. Maryška, M. Rozložník and M. Tuma. Mixed-hybrid finite element approximation of the potential fluid flow problem. J. Comput. Appl. Math., 63, 383-392, 1995.
12. C. C. Paige and M. A. Saunders. Solution of sparse indefinite systems of linear equations. SIAM J. Num. Anal., 12, 617-629, 1975.
13. T. Rusten. Iterative Methods for Mixed Finite Elements System. SIAM J. Math. Anal. Appl., 13, 887-904, 1992.
14. D. J. Silvester and A. J. Wathen. Fast iterative solution of stabilized Stokes systems, Part II: using block preconditioners. SIAM J. Numer. Anal., 31, 1352-1367, 1994.
15. A. J. Wathen and D. J. Silvester. Fast iterative solution of stabilized Stokes systems, Part I: using simple diagonal preconditioners. SIAM J. Numer. Anal., 30, 639-649, 1993.
16. A. J. Wathen, B. Fischer and D. J. Silvester. The convergence rate of the minimal residual method for the Stokes problem. Num. Mathematik, 71, 121-134, 1995.