Error analysis of an ADI splitting scheme for the inhomogeneous Maxwell equations

Johannes Eilinghoff; Roland Schnaubelt

doi:10.3934/dcds.2018248

Article Contents

2018, Volume 38, Issue 11: 5685-5709. Doi: 10.3934/dcds.2018248

This issue Previous Article Averaging principle for stochastic Kuramoto-Sivashinsky equation with a fast oscillation Next Article Local correlation entropy

Error analysis of an ADI splitting scheme for the inhomogeneous Maxwell equations

Johannes Eilinghoff and
Roland Schnaubelt^,

Department of Mathematics, Karlsruhe Institute of Technology, 76128 Karlsruhe, Germany

* Corresponding author: Roland Schnaubelt
* Corresponding author: Roland Schnaubelt

Received: November 30, 2017

Revised: May 31, 2018

Published: August 2018

The authors gratefully acknowledge financial support by the Deutsche Forschungsgemeinschaft (DFG) through CRC 1173

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Abstract

In this paper we investigate an alternating direction implicit (ADI) time integration scheme for the linear Maxwell equations with currents, charges and conductivity. We show its stability and efficiency. The main results establish that the scheme converges in a space similar to $H^{-1}$ with order two to the solution of the Maxwell system. Moreover, the divergence conditions in the system are preserved in $H^{-1}$ with order one.

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Mathematics Subject Classification: Primary: 65M12; Secondary: 35Q61, 47D06, 65J10.

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