• 论文 •

### 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

1. 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.

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

1. 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

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.

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