Error analysis of finite element methods for 3-D Maxwellʹs equations in dispersive media

We consider the time dependent Maxwellʹs equations in dispersive media on a bounded three-dimensional domain. A semi-discrete standard finite element method and a semi-discrete mixed finite element method are developed and error estimates are provided. We believe this is the first finite element error analysis carried out for Maxwellʹs equations in dispersive media.