一个二阶椭圆混合问题的三棱柱元

数学物理学报 ›› 2020, Vol. 40 ›› Issue (3): 684-693.

一个二阶椭圆混合问题的三棱柱元

赵中建^1,*(),陈绍春²

¹ 华北水利水电大学数学与统计学院郑州 450046
² 郑州大学数学与统计学院郑州 450001

收稿日期:2019-03-12 出版日期:2020-06-26 发布日期:2020-07-15
通讯作者: 赵中建 E-mail:zhaozhongjian@ncwu.edu.cn
基金资助:
国家自然科学基金(11371331)

A Triangular Prism Finite Element for the Second-Order Elliptic Mixed Problem

Zhongjian Zhao^1,*(),Shaochun Chen²

¹ School of Mathematics and Statistics, North China University of Water Resources and Electric Power, Zhengzhou 450046
² School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001

Received:2019-03-12 Online:2020-06-26 Published:2020-07-15
Contact: Zhongjian Zhao E-mail:zhaozhongjian@ncwu.edu.cn
Supported by:
the NSFC(11371331)

摘要/Abstract

摘要：

二阶椭圆混合问题的有限元方法已有很多研究，包括三角形元、矩形元、四面体元和立方体元.但对三棱柱元的研究却很少，三棱柱元兼顾三角形和矩形的优点，更加适合柱形区域，尤其是截面复杂的柱形区域.该文对二阶椭圆混合问题构造一个低阶的三棱柱元，证明了它的适定性和收敛性，给出了最优的误差估计.

关键词: 二阶椭圆问题, 混合元, BB条件, 三棱柱元

Abstract:

There are many researches on the finite element method for second-order elliptic mixed problem, including triangular element, rectangular element, tetrahedral element and cubic element. However, there are few researches on the triangular prism element. The triangular prism element has the advantages of triangular and rectangular elements, and it is more suitable for cylindrical region, especially for the cylindrical region with complex cross-section. In this paper, a lower-order conforming triangular prism element is constructed for the second-order elliptic mixed problem. Its well-posedness and convergence are proved, and the optimal error estimate is given too.

Key words: The second-order elliptic problem, Mixed finite element, BB-conditions, Triangular prism element

中图分类号:

赵中建,陈绍春. 一个二阶椭圆混合问题的三棱柱元[J]. 数学物理学报, 2020, 40(3): 684-693.

Zhongjian Zhao,Shaochun Chen. A Triangular Prism Finite Element for the Second-Order Elliptic Mixed Problem[J]. Acta mathematica scientia,Series A, 2020, 40(3): 684-693.

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