The Generalized Arrow-Hurwicz Method with Applications to Fluid Computation (Communications in Computational Physics, 2018)
In this paper, we first discuss the existence and uniqueness of a class of nonlinearsaddle-point problems, which are frequently encountered in physical models.Then, a generalized Arrow-Hurwicz method is introduced to solve such problems. Forthe 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.
Keywords: Nonlinear saddle-point problems; the generalized Arrow-Hurwicz method; convergence rate analysis; fluid computation.