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A semidiscrete mixed finite element approximation to the time dependent Maxwell’s equations on a bounded smooth domain is analyzed. A variational problem for the electric and magnetic fields in which the boundary conditions are enforced naturally is derived. Then a general convergence result for mixed methods is proven, and it is shown how this result may be used to prove various error estimates when Nédélec’s curl conforming finite elements are used.
Peter Monk (Sun,) studied this question.