关于Stokes和线性Navier-Stokes方程的广义维数分裂迭代方法

ON GENERALIZED DIMENSIONAL SPLITTING ITERATIVE METHODS FOR STOKES AND LINEARIZED NAVIER-STOKES EQUATIONS

本文研究了鞍点问题的迭代法.在Benzi等人提出的维数分裂(DS)迭代方法的基础上,提出了具有三个参数的广义维数分裂(GDS)迭代法,该方法包含了DS迭代法,理论分析表明该方法是无条件收敛的.通过对有限差分法和有限元法离散的Stokes问题及有限元法离散的Oseen问题的数值结果表明,本文所给方法是有效的.

In this paper, we,study the iterative methods for saddle point problems （SPP）. Based on the dimensional splitting（DS） which was proposed by Benzi et al., we present a gener- alized dimensional splitting（GDS） iterative methods with three parameters which cover DS methods. Theoretical analysis shows that the new method is unconditional convergence. Numerical results from discrete Stokes problems by finite difference methods and finite element methods, and discrete Oseen problems by finite element methods show that the new method is efficient.