Error analysis of DGTD for linear Maxwell equations with inhomogeneous interface conditions

TL;DR

This paper analyzes the error behavior of a discontinuous Galerkin and leapfrog scheme applied to Maxwell equations with inhomogeneous interfaces, providing theoretical error bounds and numerical validation.

Contribution

It offers the first rigorous error analysis for DGTD methods applied to Maxwell equations with inhomogeneous interface conditions.

Findings

Proved well-posedness and stability of the discretized problem.

Derived explicit error bounds for spatial and full discretization.

Numerical experiments confirm theoretical error estimates.

Abstract

In the present paper we consider linear and isotropic Maxwell equations with inhomogeneous interface conditions. We discretize the problem with the discontinuous Galerkin method in space and with the leapfrog scheme in time. An analytical setting is provided in which we show wellposedness of the problem, derive stability estimates, and exploit this in the error analysis to prove rigorous error bounds for both the spatial and full discretization. The theoretical findings are confirmed with numerical experiments.