Stokes方程的投影／方向分裂谱方法

我们提出和分析了一种求解Stokes方程的数值方法．新方法基于空间上的Legendre谱离散，时间上则采用投影／方向分裂格式．更确切地说，时间离散的出发点是旋度形式的压力校正投影法，在此基础上进一步应用方向分裂法，把速度和压力方程分裂为一系列一维的椭圆型子问题．然后生成的这些一维子问题用Legendre谱方法进行空间离散．另外，我们证明了全离散格式的稳定性．一些数值实验验证了收敛性和方法的有效性．

Spectral Methods for the Projection/Direction Stokes Equations Using Splitting Schemes

In this paper we propose and analyze a numerical method for the Stokes equations. The proposed method combines a Legendre spectral method for the spatial discretization and a projection/direction splitting scheme for the temporal discretization. Precisely, based on the rotational pressure correction projection method for the Stokes equations, a direction splitting approach is furthermore applied to split the elliptic subproblems for the velocity and for the pressure respectively, leading to a set of 1D problems. Then a Legendre spectral method is used to discretize this set of 1D problems. We prove the stability of the overall scheme in the full discrete form. Some numerical tests are carried out to confirm the convergence and efficiency of the proposed method.