New Discretization Schemes for Time-Harmonic Maxwell Equations by Weak Galerkin Finite Element Methods

TL;DR

This paper presents novel weak Galerkin finite element discretization schemes for time-harmonic Maxwell equations, providing stability, convergence analysis, and optimal error estimates in various norms.

Contribution

The paper introduces new WG finite element schemes for Maxwell equations with rigorous stability, convergence proofs, and optimal error bounds, advancing numerical methods for electromagnetic problems.

Findings

Stable and convergent WG schemes for Maxwell equations

Optimal order error estimates in discrete Sobolev norms

Theoretical validation of the proposed discretization methods

Abstract

This paper introduces new discretization schemes for time-harmonic Maxwell equations in a connected domain by using the weak Galerkin (WG) finite element method. The corresponding WG algorithms are analyzed for their stability and convergence. Error estimates of optimal order in various discrete Sobolev norms are established for the resulting finite element approximations.