速度-压力的Q_2-Q_1有限元

A NOTE ON THE BIQUADRATIC-BILINEAR VELOCITY-PRESSURE FINITE ELEMENT

本文讨论了Stokes方程的Q_2-Q_1有限元,即速度空间采用双二次分片多项式插值,压力空间采用双一次分片多项式播值.在不满足经典的Babuska-Brezzi条件下,本注记进一步讨论了混合有限元方法和简化积分的罚方法,当解光滑性加强时,分别得到最优阶误差估计式|u-u_h|=O(h_2)及|u-u_h^2|_1=O(h^(2+)),改进了G.F.Carey,J.T.Oden等的结果.

In this note we discuss the biquadratic-bilinear velocity-pressure finite element for the Stokes e-quations. Although it does not satisfy the classical Babuska-Brezzi condition, we study further the mixed finite element method and reduced integration and penalty method. The optimal error estimates |u - uh|1 = 0(h2) and |u - uh|1 = 0(h2) can be obtained if the solution becomes moresmooth. And the results have been improved on G. F. Carey and J. T. Oden.