Stokes方程非协调混合元的特征值下界

通过利用Crouzeix-Raviart元({1,x,y}),旋转元({1,x,y,x~2-y~2}),拓广旋转元({1,x,y,x~2,y~2})以及拓广Crouzeix-Raviart元({1,x,y,x~2+y~2})这四种混合有限元(参看正文中示图)来提供求Stokes特征值下界的方法.并找到恰当的理论框架,重要的是证明不仅统一,而且出奇的短,仅需几行.最后给出相关的数值结果来验证本文的理论分析.

Stokes Eigenvalue Approximations from Below with Nonconforming Mixed Finite Element Methods

We provide the lower bounds of Stokes eigenvalue by using 4 nonconforming mixed finite elements:Crouzeix-Raviart({1,x,y}),Q_1~(rot)({1,x,y,x~2 - y~2}),extension Q_1~(rot) ({1,x,y,x~2,y~2}) and extension Crouzeix-Raviart({1,x,y,x~2 +y~2}).We find a suitable theoretical framework which makes the proof unified and surprisingly short,with a few steps only! Some numerical results are used to confirm the theoretical tonvergence results.