Acta mathematica scientia,Series A ›› 2020, Vol. 40 ›› Issue (3): 684-693.

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

Zhongjian Zhao1,*(),Shaochun Chen2   

  1. 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)

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

CLC Number: 

  • O24
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