Unbounded Domains Stokes Problem Decomposition Method Based On Natural Boundary Reduction Of The Region

The Stokes problem is the classic model of fluid mechanics, scientists often encounter the problem, it is widely used in many fields. Studying Stokes problem is helpful to deal with the more complicated Navier-Stokes problems, we can also solve complex problems by computer, and find out numerical solution.Domain decomposition method is a numerical method for solving partial differential equations, and its convergence of most studies in linear partial differential equations is obtained.The domain decomposition method not only can narrow solving scale to parallel computing, but also select different discrete methods and models in different areas. Overlapping decomposition method is using Schwarz alternate method as the theory basis, Schwarz method can solve complex domain decomposition for some mutual coverage of the subdomain, in which problem can be solved quickly. Schwarz method and projection method are connected ingeniously, so convergence of proof looks complex, simplifying the estimate of projection operator. For multiple areas of overlapping subdomain, even nonlinear problem of Schwarz method is managed in unified framework.The overlapping domain decomposition method of the Stokes problem is studied on planar unbounded domains. Firstly, mixed element for settling the problem in the inner subdomain is used, the pressure and velocity are got, and then the pressure and velocity in the external domain can be worked out by the Poisson's integral formula. Through the Schwarz method, this alternating method can solve the problem of unbounded domain, and receive the numerical solution of the original problem through the initial variables. We testify the geometric convergence of the overlapping domain decomposition method. Finally numerical examples show that the conclusion is correct. For the artificial boundary element method, this paper gives the planar unbounded regional Stokes problem of Steklov-Poincare mapping and six equivalent forms, coupled with finite element method naturally, and get error estimates.