  In this work, we present a new numerical method for solving the scalar
transmission problem with sign-changing coefficients. In electromagnetism, such
a transmission problem can occur if the domain of interest is made of a
classical dielectric material and a metal or a metamaterial, with for instance
an electric permittivity that is strictly negative in the metal or
metamaterial. The method is based on an optimal control reformulation of the
problem. Contrary to other existing approaches, the convergence of this method
is proved without any restrictive condition. In particular, no condition is
imposed on the a priori regularity of the solution to the problem, and no
condition is imposed on the meshes, other than that they fit with the interface
between the two media. Our results are illustrated by some (2D) numerical
experiments.

Numerical Analysis;Numerical Analysis