论文信息 - Convergence Analysis of the Modified Nonlinear Inexact Uzawa Algorithm for Saddle Point Problem

Convergence Analysis of the Modified Nonlinear Inexact Uzawa Algorithm for Saddle Point Problem

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

Junfeng Lu

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