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

doi:10.1007/s42967-025-00504-3

Abstract

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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URL: https://www.camc.shu.edu.cn/EN/10.1007/s42967-025-00504-3

https://www.camc.shu.edu.cn/EN/Y2026/V8/I4/1366

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

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