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A coercive mixed variational formulation on H 0 ( curl ; Ω ) × H ( div ; Ω ) is proposed for the generalized Maxwell problem which typically arises from computational electromagnetism. The mixed variables are the electric field and a pseudo electric displacement field. The well-posedness of the mixed variational problem is proven in the general settings (multiply connected domain of Lipschitz-continuous boundary with a number of connected components, filling with discontinuous, anisotropic and inhomogeneous media); more importantly, the coercivity is established. A conforming finite element discretization is further proposed, where the electric field is approximated by H ( curl ; Ω ) -conforming edge element while the pseudo electric displacement field by H ( div ; Ω ) -conforming flux element. Error estimates are obtained, and in particular, the method produces an L 2 curl-convergent approximation and more importantly, an L 2 div-convergent approximation for the solution. |
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