Finite element study of the Lorentz model in metamaterials

Metamaterials are materials with electromagnetic properties that originate from artificial sub-wavelength structures. Although the Lorentz metamaterial model has been used by physicists and electrical engineers, its mathematical properties have not been investigated yet. Also more robust and efficient algorithms for time-domain simulations are needed. In this paper, we initiate our work in this respect by developing some finite element schemes for solving the Lorentz model. Stability and error analysis are proved for these schemes, and 2-D numerical results justifying our theoretical results are presented.