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四阶抛物方程H1-Galerkin混合有限元方法的超逼近及最优误差估计
引用本文:石东洋,史艳华,王芬玲.四阶抛物方程H1-Galerkin混合有限元方法的超逼近及最优误差估计[J].计算数学,2014,36(4):363-380.
作者姓名:石东洋  史艳华  王芬玲
作者单位: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
基金项目: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H1-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.

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
收稿时间:2013-09-08;

SUPERCLOSENESS AND THE OPTIMAL ORDER ERROR ESTIMATES OF H1-GALERKIN MIXED FINITE ELEMENT METHOD FOR FOURTH-ORDER PARABOLIC EQUATION
Shi Dongyang,Shi Dongyang,Wang Fenling.SUPERCLOSENESS AND THE OPTIMAL ORDER ERROR ESTIMATES OF H1-GALERKIN MIXED FINITE ELEMENT METHOD FOR FOURTH-ORDER PARABOLIC EQUATION[J].Mathematica Numerica Sinica,2014,36(4):363-380.
Authors:Shi Dongyang  Shi Dongyang  Wang Fenling
Institution:1. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China;
2. School of Mathematics and Statistics, Xuchang University, Xuchang 461000, Henan, China
Abstract:In this paper, based on bilinear element and zero-order Raviart-Thomas element (R-T), H1-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.
Keywords:Fourth-order parabolic  H1-Galerkin mixed finite element method" target="_blank">H1-Galerkin mixed finite element method')" href="#">H1-Galerkin mixed finite element method  semi-discrete and fully-discrete schemes  error estimates and supercloseness
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