Remarks on the discretization of some non-coercive operator with applications to heterogeneous Maxwell equations

We aim at providing a framework for the analysis of convergence for the Galerkin approximation for a class of noncoercive problems. We provide a sufficient condition on the finite element space for the convergence and optimality of the Galerkin scheme. This theory is then applied to the study of the well-posedness and approximability of two problems in electromagnetism.