A time-domain finite element scheme and its analysis for nonlinear Maxwell's equations in Kerr media

The purpose of this paper is to develop and analyze a finite element method for solving the time-dependent Maxwell's equations in nonlinear Kerr media. The proposed fully-discrete scheme is proved to be conditionally stable and optimally convergent in the spatial variable and second order in time. Numerical results are presented to support our theoretical analysis and also to demonstrate the practical soliton propagation phenomena in Kerr media. (c) 2021 Elsevier Inc. All rights reserved.

Automated summary

This paper introduces a finite element method for solving the time-dependent Maxwell's equations in nonlinear Kerr media. The fully-discrete scheme is shown to be conditionally stable in the spatial variable and second order in time. Numerical results support the theoretical analysis and demonstrate practical soliton propagation phenomena in Kerr media.