Fast uzawa algorithm for generalized saddle point problems

Authors:
Zhi-Hao Cao
Affiliations:
Department of Mathematics and Laboratory of Mathematics for Nonlinear Sciences, Fudan University, Shanghai 200433, People's Republic of China
Venue:
Applied Numerical Mathematics
Year:
2003

Citing 7
Cited 12

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Analysis of the nonlinear Uzawa algorithm for symmetric saddle point problems

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Parameterized preconditioning for generalized saddle point problems arising from the Stokes equation

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Abstract

In SIAM J. Numer. Anal. 34 (1997) 1072, the authors considered the so-called "inexact Uzawa" algorithm for iteratively solving saddle point problems. In this paper, we consider the same algorithm for iteratively solving generalized saddle point problems. Our main concern is how to accelerate the convergence of the inexact Uzawa algorithm. The new contributions of the paper are that a new nonlinear Uzawa algorithm is derived and its convergence is analyzed. Applications to Stokes equations by mixed finite element discretization with an unstable pair of approximation spaces, i.e., Q1 - P0 pair of approximation spaces, are discussed and the results of the numerical experiments are presented.