# A hybridizable discontinuous Galerkin method for the indefinite time-harmonic Maxwell equations

## TL;DR

This paper develops a hybridizable discontinuous Galerkin (HDG) method for solving the indefinite time-harmonic Maxwell equations in 3D, providing error estimates independent of the wavenumber and validated by numerical tests.

## Contribution

The paper introduces a novel HDG method for Maxwell equations with explicit wavenumber regularity and a discrete inf-sup condition, ensuring stability and optimal error estimates.

## Key findings

- Error estimates are independent of the wavenumber.
- The method is stable for all mesh sizes and domain shapes.
- Numerical experiments confirm theoretical predictions.

## Abstract

In this paper, we aim to develop a hybridizable discontinuous Galerkin (HDG) method for the indefinite time-harmonic Maxwell equations with the perfectly conducting boundary in the three-dimensional space. First, we derive the wavenumber explicit regularity result, which plays an important role in the error analysis for the HDG method. Second, we prove a discrete inf-sup condition which holds for all positive mesh size $h$, for all wavenumber $k$, and for general domain $\Omega$. Then, we establish the optimal order error estimates of the underlying HDG method with constant independent of the wavenumber. The theoretical results are confirmed by numerical experiments.