(untitled) (Communications in Computational Physics, 2018)
In this paper, we first discuss the existence and uniqueness of a class of nonlinear saddle-point problems, which are frequently encountered in physical models. Then, a generalized Arrow-Hurwicz method is introduced to solve such problems. For the method, the convergence rate analysis is established under some reasonable conditions. It is also applied to solve three typical discrete methods in fluid computation, with the computational efficiency demonstrated by a series of numerical experiments.