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

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 ${\mathbb {R}}^d\;(d=2, 3).$ The super-convergence of order one for the discrete $\textbf{H}^1$-like norm has been established. Numerical simulations show that the approximate solutions converge to the exact solutions with optimal rates in the $L^2$ norm on hybrid meshes. In addition, this method is shown to be absolutely stable under low regularity requirements with high wave numbers.

Keywords

Least-squares / Weak Galerkin (WG) / Finite-element method / Maxwell’s equations / Polygonal/Polyhedral meshes / Primary: 65N15 / 65N30 / 76D07 / Secondary: 35B45 / 35J50

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