On fictitious domain formulations for Maxwell's equations

We consider fictitious domain-Lagrange multiplier formulations for variational problems in the space H(curl: Omega) derived from Maxwell's equations. Boundary conditions and the divergence constraint are imposed weakly by using Lagrange multipliers. Both the time dependent and time harmonic formulations of the Maxwell's equations are considered. and we derive well-posed formulations for both cases. The variational problem that arises can be discretized by functions that do not satisfy an a-priori divergence constraint.