A discontinuous Galerkin method for Maxwell's transmission eigenvalue problem

We propose an interior penalty discontinuous Galerkin (IPDG) method for the Maxwell's transmission eigenvalue problem. First we reformulate the problem as a parameterized eigenvalue problem and define the fixed-point function. The well-posedness of the IPDG discretization for the source problem is proved. Then the uniform convergence of the parameterized discrete solution operator is proved. Finally the error analysis for the IPDG method is realized under reasonable assumptions on the fixed-point function. Numerical examples in 2D and 3D are presented for validation.