四阶拋物方程H^1-Galerkin混合有限元方法的超逼近及最优误差估计

SUPERCLOSENESS AND THE OPTIMAL ORDER ERROR ESTIMATES OF H^1-GALERKIN MIXED FINITE ELEMENT METHOD FOR FOURTH-ORDER PARABOLIC EQUATION

本文基于双线性元及零阶Raviart-Thomas元(R-T)对四阶抛物方程建立了半离散和向后欧拉全离散H^1-Galerkin混合有限元格式.利用积分恒等式技巧和单元的特殊构造,证明了关于上述两元的两个新的重要性质.进而导出了这两种格式下相关变量的最优误差估计和超逼近性质.

In this paper, based on bilinear element and zero-order Raviart-Thomas element （R-T）, Hl-Galerkin mixed finite element schemes are established for fourth-order parabolic equation in semi-discrete and Back-Euler fully-discrete cases. By use of integral identity technique and the special construction of elements, two new important properties of the above two elements are proved. Furthermore, the optimal order error estimates and superclose properties of the corresponding variables are deduced for the above two schemes.