A class of iterative methods for solving saddle point problems

Randolph E. Bank; Bruno D. Welfert; Harry Yserentant

doi:10.1007/bf01405194

journal article Jul 01, 1989

A class of iterative methods for solving saddle point problems

Randolph E. Bank Bruno D. Welfert Harry Yserentant

Numerische Mathematik Vol. 56 No. 7 pp. 645-666 · Springer Science and Business Media LLC

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References

20

[1]

Arnold, D.N., Brezzi, F., Fortin, M. Astable finite element for the Stokes equations. Calcolo21, 337?344 (1984) 10.1007/bf02576171

[2]

Aziz, A.K., Babu?ka I.: Part I, 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, pp. 1?362. New York: Academic Press 1972

[3]

Bank, R.E., Dupont, T.F.: Analysis of a two level scheme for solving finite element equations. Tech. Rep. CNA-159, Center for Numerical Analysis, University of Texas at Austin 1980 10.2118/7683-ms

[4]

Bank, R.E., Dupont, T.F., Yserentant, H.: The hierarchical basis multigrid method. Numer. Math.52, 427?458 (1988) 10.1007/bf01462238

[5]

Bramble, J.H., Pasciak, J.E.: A preconditioning technique for indefinite systems resulting from mixed approximations of elliptic problems. Math. Comput.181, 1?17 (1988) 10.1090/s0025-5718-1988-0917816-8

[6]

Brezzi, F.: On the existence, uniqueness and approximation of saddle-point problems arising from Lagrange multipliers. R.A.I.R.O.8, 129?151 (1974)

[7]

Axelsson, O.: Preconditioning indefinite problems by regularization. SIAM J. Numer. Anal.16, 58?69 (1979) 10.1137/0716005

[8]

Dyn, N., Ferguson, W.E.: Numerical solution of equality constrained quadratic programming problems. Math. Comput.41, 165?170 (1983)

[9]

Girault, V., Raviart, P.: Finite element methods for Navier-Stokes equations. Berlin Heidelberg New York: Springer 1986 10.1007/978-3-642-61623-5

[10]

Golub, G.H., Overton, M.L.: The convergence of inexact Chebyshev and Richardson iterative methods for solving linear systems. Numer. Math.53, 571?593 (1988) 10.1007/bf01397553

[11]

Multi-Grid Methods and Applications

Wolfgang Hackbusch

Springer Series in Computational Mathematics 1985 10.1007/978-3-662-02427-0

[12]

Maitre, J.F., Musy, F., Nigon, P.: A fast solver for the Stokes equations using multigrid with a Uzawa smoother, In: Notes on numerical fluid mechanics, pp. 77?83. Braunschweig: Vieweg 1985

[13]

McCormick, S. (Editor): Multigrid methods. SIAM, Philadelphia 1987

[14]

Verfürth, R.: A combined conjugate gradient-multigrid algorithm for the numerical solution of the Stokes problem. IMA J. Numer. Anal.4, 441?455 (1984) 10.1093/imanum/4.4.441

[15]

Verfürth, R.: Iterative methods for the numerical solution of mixed finite element approximations of the Stokes problem. Tech. Rep. 379, Institut National de Recherche en Informatique et en Automatique 1985

[16]

Verfürth, R.: A multilevel algorithm for mixed problems. SIAM J. Numer. Anal.21, 264?271 (1984) 10.1137/0721019

[17]

Verfürth, R.: A multilevel algorithm for mixed problems. II. treatment of the mini-element. SIAM J. Numer. Anal.25, 285?293 (1988) 10.1137/0725020

[18]

Wittum, G.: Multigrid methods for Stokes and Navier stokes equations. Transforming smoothers: algorithms and numerical results. Numer. Math.54, 543?563 (1989) 10.1007/bf01396361

[19]

Wittum, G.: On the convergence of multigrid methods with transforming smoothers: theory with applications to the Navier-Stokes equations. Tech. Rep. 468, Sonderforschungsbereich 123, Universität Heidelberg 1988

[20]

On the multi-level splitting of finite element spaces

Harry Yserentant

Numerische Mathematik 1986 10.1007/bf01389538

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Published: Jul 01, 1989
Vol/Issue: 56(7)
Pages: 645-666
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Randolph E. Bank, Bruno D. Welfert, Harry Yserentant (1989). A class of iterative methods for solving saddle point problems. Numerische Mathematik, 56(7), 645-666. https://doi.org/10.1007/bf01405194

A class of iterative methods for solving saddle point problems

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