ANALYSIS OF A QUADRILATERAL EDGE ELEMENT METHOD FOR MAXWELL EQUATIONS

  • Zhijie DU1 ,
  • Huoyuan DUAN2 ,
  • * ,
  • Caihong WANG2
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  • 1. School of Mathematics and Statistics, Wuhan University of Technology, Wuhan 430070, China;
    2. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
Zhijie DU, E-mail: zjdu@whu.edu.cn;Caihong WANG, E-mail: 1473913822@qq.com

Received date: 2024-07-30

  Revised date: 2024-11-06

  Online published: 2026-05-22

Supported by

National Natural Science Foundation of China (12401482) and the second author was supported by the National Natural Science Foundation of China (12371371, 12261160361, 11971366). This work was supported by the Open Research Fund of Hubei Key Laboratory of Computational Science, Wuhan University.

Abstract

A new quadrilateral edge element method is proposed and analyzed for Maxwell equations. This proposed method is based on Duan-Liang quadrilateral element (Math. Comp. 73(2004), pp. 1-18). When applied to the eigenvalue problem, the method is spectral-correct and spurious-free. Stability and error estimates are obtained, including the interpolation error estimates and the error estimates between the finite element solution and the exact solution. The method is suitable for singular solution as well as smooth solution, and consequently, the method is valid for nonconvex domains which may have a number of reentrant corners. Of course, the method is suitable for arbitrary quadrilaterals (under the usual shape-regular condition).

Cite this article

Zhijie DU1 , Huoyuan DUAN2 , * , Caihong WANG2 . ANALYSIS OF A QUADRILATERAL EDGE ELEMENT METHOD FOR MAXWELL EQUATIONS[J]. Acta mathematica scientia, Series B, 2026 , 46(1) : 275 -292 . DOI: 10.1007/s10473-026-0116-3

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