Analysis of a direct discretization of the Maxwell eigenproblem

A direct discretization is analyzed for the computation of the eigenvalues of the Maxwell eigenproblem, where the finite element space (P-k)(d) + del Pk+1 with the pair of the kth order P-k and (k + 1)th order Pk+1 Lagrange element spaces (k >= 1) on generic simplexes are used. The finite element space directly mimics the Hodge decomposition of the second-kind kth order Nedelec (P-k)(d) elements while the finite element formulation directly uses the classical variational formulation. We prove the convergence of the resulting finite element solutions.