四阶障碍问题的稳定化混合有限元方法

Stabilized Mixed Finite Element Approximation for Fourth Order Obstacle Problem

本文讨论了四阶障碍问题的稳定化混合有限元方法.首先,引入网格依赖范数,通过加罚方法得到了与四阶障碍问题的等价的混合变分形式.随后给出了基于C^O协调有限元空间(W_h,V_h)的混合有限元逼近,例如P_k-P_k三角形有限元.在网格依赖范数下,(W_h,V_h)满足离散的inf-sup条件.最后,我们在不同的假设下,得到了一些误差估计.

The stabilized mixed finite element approximation for fourth order obstacle problem is investigated in this paper. Firstly, the mesh dependent norms are introduced and the equivalent mixed variational problem of the fourth order obstacle problem is derived by the penalty method. Subsequently, the mixed finite element approximation based on the CO conforming finite element subspaces （Wh, Vh） like the Pk - Pk triangle element is proposed. Under these mesh dependent norms, （Wh, Vh） satisfy the discrete inf-sup conditions. Finally, we obtain some error estimates under the different assumptions.