Semi-convergence analysis of the GPIU method for singular nonsymmetric saddle-point problems

Abstract

In this paper, the generalized parameterized inexact Uzawa (GPIU) method is further investigated for solving singular nonsymmetric saddle-point problems. The semi-convergence conditions of this method are derived, which further develop the results obtained in the paper Zhang and Wang, Appl. Math. Comput. 219(9), 4225-4231 (2013). Furthermore, the theoretical results are confirmed by a steady-state Navier-Stokes problem. Numerical experiments demonstrate that the GPIU method is feasible and effective for the 'leaky' lid-driven cavity problems with higher viscosity constants, i.e., singular nonsymmetric saddle-point problems with positive real and symmetric dominant (1,1) part.