Resolution of the Maxwell equations in a domain with reentrant corners

In the case when the computational domain is a polygon with reentrant corners, we give a decomposition of the solution of Maxwell's equations into the sum of a regular part and a singular part. It is proved that the space to which the singular part belongs is spanned by the solutions of a steady state problem. The precise regularity of the solution is given depending on the angle of the reentrant corners. The mathematical decomposition is then used to introduce an algorithm for the numerical resolution of Maxwell's equations in presence of reentrant corners. This paper is a continuation of the work exposed in [3]. The same methodology can be applied to the Helmholtz equation or to the Lamé system as well.