各向异性网格下抛物方程一个新的非协调混合元收敛性分析

doi:10.12286/jssx.2013.2.171

计算数学 ›› 2013, Vol. 35 ›› Issue (2): 171-180.DOI: 10.12286/jssx.2013.2.171

各向异性网格下抛物方程一个新的非协调混合元收敛性分析

张亚东¹, 石东洋²

1. 许昌学院数学与统计学院, 河南许昌 461000;
2. 郑州大学数学系, 郑州 450052

收稿日期:2012-09-04 出版日期:2013-05-15 发布日期:2013-05-13
通讯作者: 石东洋
基金资助:
国家自然科学基金(10971203; 11271340)和高等学校博士学科点专项基金(2009410111006)资助项目.

PDF ( 1398 ) 引用被引次数 ( 22 | 5 )

张亚东, 石东洋. 各向异性网格下抛物方程一个新的非协调混合元收敛性分析[J]. 计算数学, 2013, 35(2): 171-180.

Zhang Yadong, Shi Dongyang. CONVERGENCE ANALYSIS OF A NEW NONCONFORMING MIXED FINITE ELEMENT FOR PARABOLIC EQUATION ON ANISOTROPIC MESH[J]. Mathematica Numerica Sinica, 2013, 35(2): 171-180.

CONVERGENCE ANALYSIS OF A NEW NONCONFORMING MIXED FINITE ELEMENT FOR PARABOLIC EQUATION ON ANISOTROPIC MESH

Zhang Yadong¹, Shi Dongyang²

1. School of Mathematics and Statistics, Xuchang University, Xuchang 461000, Henan, China;
2. Department of Mathematics, Zhengzhou University, Zhengzhou 450052, China

Received:2012-09-04 Online:2013-05-15 Published:2013-05-13

本文将 Crouzeix-Raviart 型非协调线性三角形元应用到抛物方程,建立了一个新的混合元格式.在抛弃传统有限元分析的必要工具 Ritz 投影算子的前提下,直接利用单元的插值性质和导数转移技巧, 分别得到了各向异性剖分下关于原始变量u 的H^-1-模和积分意义下L²-模以及通量p=-▽u 在L²-模下的最优阶误差估计.数值结果与我们的理论分析是相吻合的.

关键词： 抛物方程, 非协调元, 新混合元格式, 各向异性网格, 收敛性分析

In this paper, a Crouzeix-Raviart type nonconforming linear triangular finite element is applied to the parabolic equation and a new mixed element formulation is established. By utilizing the properties of the interpolation on the element and derivative delivery techniques instead of the Ritz projection operator, which is an indispensable tool in the traditional finite element analysis, the optimal order error estimates for the primitive solution u in broken H¹−norm and L²-norm with integral and the flux p=-▽u in L²-norm are obtained on anisotropic meshes, respectively. The numerical results show the validity of the theoretical analysis.

Key words: parabolic equation, nonconforming finite element, new mixed finite element, anisotropic meshes, convergence analysis

MR(2010)主题分类:

65N15
65N30

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摘要

各向异性网格下抛物方程一个新的非协调混合元收敛性分析

CONVERGENCE ANALYSIS OF A NEW NONCONFORMING MIXED FINITE ELEMENT FOR PARABOLIC EQUATION ON ANISOTROPIC MESH

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