Convergence Analysis of the Modified Nonlinear Inexact Uzawa Algorithm for Saddle Point Problem
نویسنده
چکیده
This paper focuses on the convergence of the modified nonlinear inexact Uzawa algorithm (MNIU) for solving the saddle point problem. We improve the sufficient conditions for convergence and the convergence rate shown in Bramble et al. [J. Bramble, J. Pasciak, and A. Vassilev, Analysis of the inexact Uzawa algorithm for saddle point problems, SIAM J. Numer. Anal., 34 (1997), pp. 1072–1092] and Ye et al. [H. Ye and X. Cheng, Some remarks on the nonlinear inexact Uzawa algorithm for saddle point problem, Internat. J. Comput. Math., 82(1)(2005), pp. 89–96]. We also formulate the optimal over-relaxation parameter for speeding up the convergence of MNIU. Numerical experiments are reported to illustrate the theoretical results. Mathematics Subject Classification: 65F10, 65F50, 65N22
منابع مشابه
A modified inexact Uzawa A lgorithm for generalized saddle point problems
In this note, we discuss the convergence behavior of a modified inexact Uzawa algorithm for solving generalized saddle point problems, which is an extension of the result obtained in a recent paper [Z.H. Cao, Fast Uzawa algorithm for generalized saddle point problems, Appl. Numer. Math., 46 (2003) 157-171]. Keywords—Saddle point problem; Inexact Uzawa algorithm; Convergence behavior.
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