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.

中文翻译：

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Kerr介质中非线性Maxwell方程的时域有限元格式及其分析

本文的目的是开发和分析一种求解非线性Kerr介质中与时间有关的Maxwell方程的有限元方法。所提出的全离散方案被证明是条件稳定的，并且在空间变量和二阶时间上是最优收敛的。给出数值结果以支持我们的理论分析，并证明实际的孤子在Kerr介质中的传播现象。