On Preconditioned Uzawa-type Iterations for a Saddle Point Problem with Inequality Constraints
作者： Carsten Gräser , Ralf Kornhuber
DOI: 10.1007/978-3-540-34469-8_8
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摘要: We consider preconditioned Uzawa iterations for a saddle point problem with inequality constraints as arising from an implicit time discretization of the Cahn-Hilliard equation obstacle potential. present new class preconditioners based on linear Schur complements associated successive approximations coincidence set. In numerical experiments, we found superlinear convergence and finite termination.
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Stephen J. Wright, Primal-Dual Interior-Point Methods ,(1987)
C. M. Elliott, The Cahn-Hilliard Model for the Kinetics of Phase Separation Birkhäuser Basel. pp. 35- 73 ,(1989) , 10.1007/978-3-0348-9148-6_3
Ivar Ekeland, Roger Téman, Convex analysis and variational problems ,(1976)
Ralf Kornhuber, Monotone multigrid methods for elliptic variational inequalities I Numerische Mathematik. ,vol. 69, pp. 167- 184 ,(1994) , 10.1007/BF03325426
Howard C. Elman, Gene H. Golub, Inexact and preconditioned Uzawa algorithms for saddle point problems SIAM Journal on Numerical Analysis. ,vol. 31, pp. 1645- 1661 ,(1994) , 10.1137/0731085
H. Weinert, Ekeland, I. / Temam, R., Convex Analysis and Variational Problems. Amsterdam-Oxford. North-Holland Publ. Company. 1976. IX, 402 S., Dfl. 85.00. US $ 29.50 (SMAA 1) ZAMM - Zeitschrift für Angewandte Mathematik und Mechanik. ,vol. 59, pp. 282- 282 ,(1979) , 10.1002/ZAMM.19790590621
Walter Zulehner, Analysis of iterative methods for saddle point problems: a unified approach Mathematics of Computation. ,vol. 71, pp. 479- 505 ,(2002) , 10.1090/S0025-5718-01-01324-2
James H. Bramble, Joseph E. Pasciak, Apostol T. Vassilev, Analysis of the Inexact Uzawa Algorithm for Saddle Point Problems SIAM Journal on Numerical Analysis. ,vol. 34, pp. 1072- 1092 ,(1997) , 10.1137/S0036142994273343
R. Glowinski, Jacques Louis Lions, Raymond Trémolières, Numerical Analysis of Variational Inequalities ,(1981)
Xiaojun Chen, On preconditioned Uzawa methods and SOR methods for saddle-point problems Journal of Computational and Applied Mathematics. ,vol. 100, pp. 207- 224 ,(1998) , 10.1016/S0377-0427(98)00197-6