# Semi-discrete finite element approximation applied to Maxwell's equations in nonlinear media

## TL;DR

This paper investigates a semi-discrete finite element method for Maxwell's equations in nonlinear Kerr media, providing error estimates for Nédélec element approximations.

## Contribution

It introduces a priori error estimates for finite element approximations of Maxwell's equations in nonlinear media using Nédélec elements.

## Key findings

- A priori error estimates are established for the finite element approximation.
- The method is applicable to Maxwell's equations in Kerr-type nonlinear media.
- The analysis confirms the effectiveness of Nédélec elements in this context.

## Abstract

In this paper the semi-discrete finite element approximation of initial boundary value problems for Maxwell's equations in nonliear media of Kerr-type is investigated. For the case of N\'ed\'elec elements from the first family, a priori error estimates are established for the approximation.