Adaptive algorithm for an inverse electromagnetic scattering problem

In this article we present an a posteriori error estimate together with adaptive algorithm for an inverse electromagnetic scattering problem. The inverse problem is formulated as an optimal control problem, where we solve equations expressing stationarity of an associated Lagrangian. The a posteriori error estimate for the Lagrangian couples residuals of the computed solution to weights of the reconstruction. We show that the weights can be obtained by solving an associated linearized problem for the Hessian of the Lagrangian. The performance of the adaptive finite element method and the usefulness of the a posteriori error estimate are illustrated in numerical examples.