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

作　　者：石东洋[1] 史艳华[2] 王芬玲[2] 

机构地区：[1]郑州大学数学与统计学院,郑州450001 [2]许昌学院数学与统计学院,河南许昌461000

出　　处：《计算数学》2014年第4期363-380,共18页Mathematica Numerica Sinica

基　　金：国家自然科学基金(10971203;11271340;11101381);河南省教育厅资助基金(14A110009);许昌学院青年骨干教师项目

摘　　要：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.

关 键 词：四阶抛物方程 H1-Galerkin混合有限元方法 半离散和全离散 误差估计及超逼近 

分 类 号：O241.82[理学—计算数学]