A Mixed Method for Maxwell Eigenproblem

We propose a mixed method for the computation of the eigenvalues of the Maxwell eigenproblem, in terms of the electric field and a multiplier. The method allows the Lagrange elements of any order greater than or equal to two for the electric field, while a piecewise constant element always for the multiplier. We show that optimal error estimates yield for singular as well as smooth solutions. For the Maxwell eigenproblem in L-shaped domain which has singular and smooth eigenfunctions, we present numerical results for illustrating the effectiveness of the proposed method and for confirming the theoretical results.