# Numerical validation of an explicit P1 finite-element scheme for Maxwell's equations in a polygon with variable permittivity away from its boundary

## TL;DR

This paper numerically validates an explicit finite-element scheme for Maxwell's equations with variable permittivity in a polygon, confirming optimal convergence under the CFL condition through 2D experiments.

## Contribution

It provides empirical validation of an explicit P1 finite-element scheme for Maxwell's equations with variable permittivity, extending prior theoretical analysis.

## Key findings

- Convergence results are optimal when CFL condition is satisfied.
- Numerical experiments confirm the theoretical reliability of the scheme.
- The scheme effectively handles variable permittivity away from the boundary.

## Abstract

This paper is devoted to the numerical validation of an explicit finite-difference scheme for the integration in time of Maxwell's equations in terms of the sole electric field, using standard linear finite elements for the space discretization. The rigorous reliability analysis of this numerical model was the object of another authors' arXiv paper. More specifically such a study applies to the particular case where the electric permittivity has a constant value outside a sub-domain, whose closure does not intersect the boundary of the domain where the problem is defined. Our numerical experiments in two-dimension space certify that the convergence results previously derived for this approach are optimal, as long as the underlying CFL condition is satisfied.