非定常不可压Navier-Stokes方程两重网格方法的稳定性和L^2误差估计

L^2 ERROR ESTIMATE AND STABILITY OF A TWO-GRID METHOD FOR THE UNSTEADY INCOMPRESSIBLE NAVIER-STOKES EQUATIONS

讨论了二维非定常不可压Navier-Stokes方程的两重网格方法．此方法包括在粗网格上求解一个非线性问题,在细网格上求解一个Stokes问题．采用一种新的全离散(时间离散用Crank-Nicolson格式,空间离散用混合有限元方法)格式数值求解N-S方程．证明了该全离散格式的稳定性．给出了L2误差估计．对比标准有限元方法,在保持同样精度的前提下,TGM能节省大量的计算量．

A two-grid method for the unsteady Navier-Stokes equations modelling viscous incompressible flow is discussed in R^2, which consists of finding a solution for a nonlinear problem on a coarse grid and a solution for the Stokes problem on a fine grid. A new fully discrete scheme for the numerical solution of these equations is also considered where the spatial discreteness is the mixed finite elements and the temporal discreteness is the Crank-Nicolson scheme. The stability for this scheme is proved and an L2 error estimate is also given. Compared with the usual finite element method, this method can save a lot of computation time under the same convergence accuracy.