Fast Uzawa algorithm for generalized saddle point problems Original Research Article

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.