Analysis of a time-domain finite element method for 3-D Maxwell’s equations in dispersive media

Abstract

We consider the time dependent Maxwell’s equations in dispersive media on a bounded domain in three-dimensional space. A fully discrete finite element scheme is developed to approximate the electric field equation derived from the Maxwell’s equations. Optimal energy-norm error estimates are proved for Nédélec curl-conforming edge elements. This is the first finite element error analysis for Maxwell’s equations in dispersive media.