Abstract
In [A new nonlinear Uzawa algorithm for generalized saddle point problems, Appl. Math. Comput., 175(2006), 1432–1454], a nonlinear Uzawa algorithm for solving symmetric saddle point problems iteratively, which was defined by two nonlinear approximate inverses, was considered. In this paper, we extend it to the nonsymmetric case. For the nonsymmetric case, its convergence result is deduced. Moreover, we compare the convergence rates of three nonlinear Uzawa methods and show that our method is more efficient than other nonlinear Uzawa methods in some cases. The results of numerical experiments are presented when we apply them to Navier-Stokes equations discretized by mixed finite elements.
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Dedicated to Prof. Zhi-Hao Cao on the occasion of his 70th Birthday
Yiqin Lin is supported by Scientific Research Startup Foundation of Sun Yat-Sen University for Young Teacher under grant 2005-34000-1131042. Yimin Wei is supported by the National Natural Science Foundation of China under grant 10471027 and Shanghai Education Committee.
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Cao, Y., Lin, Y. & Wei, Y. Nonlinear uzawa methods for solving nonsymmetric saddle point problems. J. Appl. Math. Comput. 21, 1–21 (2006). https://doi.org/10.1007/BF02896385
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DOI: https://doi.org/10.1007/BF02896385