A Least-Squares-Based Weak Galerkin Finite-Element Method for the Time-Harmonic Maxwell’s Equations

doi:10.1007/s42967-025-00504-3

Communications on Applied Mathematics and Computation ›› 2026, Vol. 8 ›› Issue (4): 1366-1392.doi: 10.1007/s42967-025-00504-3

A Least-Squares-Based Weak Galerkin Finite-Element Method for the Time-Harmonic Maxwell’s Equations

Raman Kumar, Bhupen Deka

Department of Mathematics, Indian Institute of Technology Guwahati, North Guwahati, 781039, India

收稿日期:2024-09-22 修回日期:2025-05-05 接受日期:2025-05-19 出版日期:2026-08-20 发布日期:2026-09-17
通讯作者: Bhupen Deka, Email: bdeka@iitg.ac.in E-mail:bdeka@iitg.ac.in
基金资助:
The authors are grateful to the anonymous referees for valuable comments and suggestions which greatly improved the presentation of this paper.

A Least-Squares-Based Weak Galerkin Finite-Element Method for the Time-Harmonic Maxwell’s Equations

Raman Kumar, Bhupen Deka

Department of Mathematics, Indian Institute of Technology Guwahati, North Guwahati, 781039, India

Received:2024-09-22 Revised:2025-05-05 Accepted:2025-05-19 Online:2026-08-20 Published:2026-09-17
Supported by:
The authors are grateful to the anonymous referees for valuable comments and suggestions which greatly improved the presentation of this paper.

摘要/Abstract

摘要： In this article, we propose and analyze a least-squares-based weak Galerkin finite-element method (WG-FEM) for solving the indefinite time-harmonic Maxwell’s equations in R^d(d=2, 3). The super-convergence of order one for the discrete H¹-like norm has been established. Numerical simulations show that the approximate solutions converge to the exact solutions with optimal rates in the L² norm on hybrid meshes. In addition, this method is shown to be absolutely stable under low regularity requirements with high wave numbers.

关键词: Least-squares, Weak Galerkin (WG), Finite-element method, Maxwell’s equations, Polygonal/Polyhedral meshes

Abstract: In this article, we propose and analyze a least-squares-based weak Galerkin finite-element method (WG-FEM) for solving the indefinite time-harmonic Maxwell’s equations in R^d(d=2, 3). The super-convergence of order one for the discrete H¹-like norm has been established. Numerical simulations show that the approximate solutions converge to the exact solutions with optimal rates in the L² norm on hybrid meshes. In addition, this method is shown to be absolutely stable under low regularity requirements with high wave numbers.

Key words: Least-squares, Weak Galerkin (WG), Finite-element method, Maxwell’s equations, Polygonal/Polyhedral meshes

Raman Kumar, Bhupen Deka. A Least-Squares-Based Weak Galerkin Finite-Element Method for the Time-Harmonic Maxwell’s Equations[J]. Communications on Applied Mathematics and Computation, 2026, 8(4): 1366-1392.

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A Least-Squares-Based Weak Galerkin Finite-Element Method for the Time-Harmonic Maxwell’s Equations

A Least-Squares-Based Weak Galerkin Finite-Element Method for the Time-Harmonic Maxwell’s Equations

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