关于Stokes方程不满足inf-sup条件的加罚有限元方法

The penalized finite element method for the Stokes equations to circumvent the inf-sup condition

目的讨论二维不可压缩Stokes方程基于等阶有限元R1-R1元的加罚有限元方法。方法在一定的正则性条件下,利用加罚有限元方法从理论上证明其收敛性。结果加罚有限元方法对于低等阶有限元R1-R1具有很好的稳定性。结论加罚有限元方法是一种行之有效的方法。

Aim The penalized finite element method is considered for the incompressible Stokes equations on two-dimensional domain,based on some lowest equal-order finite elements space pair（Xh, Mh） which do not satisfy the discrete inf-sup condition. Method The penalized finite element method is derived under some reqularity assumptions. Then, the convergence of the penalty method is obtained. Result The penlized method are excellently stable for the lowest equal-order finite element R1 --R1. Conclusion The penalized finite element method is a better method.