The Study Of Iterative Methods For Time-Dependent Stokes Equations

The problem of solving time-dependent Stokes equations is deeply popular among scholars because it has broad application background in physics, discrete dynamic system, scientific computing, and other fields. But time-dependent Stokes equations are time-dependent partial differential equations, so they are very difficult to solve in practice. And so far only a few simple problems can obtain exact solutions. In most cases, we merely receive numerical solution of time-dependent equations by adopting iteration methods after discreting them. Therefore, it is particularly important to study the efficient numerical methods for time-dependent Stokes equations.In recent years, the issue has become a hot research of many scholars, and they have proposed some effective iterative methods, for example, TPSOR method, SOR-like method, Uzawa method(or preconditioned Uzawa method), MINRES method, a parallel finite element algorithm based on fully overlapping domain decomposition for the time-dependent Stokes equations, PCG method, CABSOR method, DABSOR method and so on.In this paper, we mainly study dual preconditioned method and its parameter form for time-dependent Stokes equations. First, we put forward dual preconditioned method and its parameter for numerical solution of time-dependent Stokes equations, and it is a new method of generalized SOR class based on the preconditioned technology. Second, we study their iterative formats and domains of convergence, respectively. Simultaneously, we get the corresponding theorems and conclutions. Finally, we give numerical examples to verify the feasibility and effectiveness of the two methods.