定常不可压阀Navier-Stokes方程的两重网格算法

A Two-grid Method for the Steady Incompressible Penalized Navier-Stokes Equations

分析了定常不可压阀Navier-Stokes(N-S)方程两重网格算法(TGM)的收敛性.给出了误差估计.得出了如果粗细网格尺寸h和H满足H=O(h3-1s)(s=0(n=2);s=12(n=3))时,这种算法和标准有限元算法(FEM)具有相同的收敛精度,但是由于TGM的简单运算,节省了计算量.给出了试验数值,验证了理论分析的正确性.

A two-grid method （TGM） of the steady incompressible penalized Navier-Stokes equations is analyzed and an error estimate is given. If the coarse size H and the fine size h satisfy H=O（h1/3-s） （s= 0（n=2） ;s=1/2（n=3）） this method has the same. convergence accuracy as the usual finite element method （FEM）. But TGM can save a lot of computation time for its brief calculation. Moreover, a numerical test is given to verify the above results.