Mixed discontinuous Galerkin approximation of the Maxwell operator: The indefinite case

We introduce and analyze a discontinuous Galerkin discretization of the Maxwell operator in mixed form. Here, all the unknowns of the underlying system of partial differential equations are approximated by discontinuous finite element spaces of the same order. For piecewise constant coefficients, the method is shown to be stable and optimally convergent with respect to the mesh size. Numerical experiments highlighting the performance of the proposed method for problems with both smooth and singular analytical solutions are presented.

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