  In this paper, we propose a weak Galerkin (WG) finite element method for the
Maxwell eigenvalue problem. By restricting subspaces, we transform the mixed
form of Maxwell eigenvalue problem into simple elliptic equation. Then we give
the WG numerical scheme for the Maxwell eigenvalue problem. Furthermore, we
obtain the optimal error estimates of arbitrarily high convergence order and
prove the lower bound property of numerical solutions for eigenvalues.
Numerical experiments show the accuracy of theoretical analysis and the
property of lower bound.
