Regularity and approximation of systems arising in electromagnetic interrogation of dielectric materials

In this paper we are concerned with a mathematical model which describes the electromagnetic interrogation of dielectric materials. We address the well-posedness of the system and regularity of solutions. Then we propose a semi-discrete nite element scheme for approximating the system and prove weak convergence under very mild regularity assumptions on the solutions of the original system. We also establish that the solution has higher regularity in time even though the input source may be a windowed signal of distributional type. This regularity is then utilized to show the strong convergence of the nite element solution.