# American Institute of Mathematical Sciences

November  2018, 38(11): 5685-5709. doi: 10.3934/dcds.2018248

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

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

* Corresponding author: Roland Schnaubelt

Received  December 2017 Revised  June 2018 Published  August 2018

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

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.

Citation: Johannes Eilinghoff, Roland Schnaubelt. Error analysis of an ADI splitting scheme for the inhomogeneous Maxwell equations. Discrete & Continuous Dynamical Systems - A, 2018, 38 (11) : 5685-5709. doi: 10.3934/dcds.2018248
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