  The Helmholtz transmission eigenvalue problem has received much concern in
materials science, so it's significant to explore the efficient calculational
method of the problem to mathematics and mechanics community. In this paper,
based on a variational formulation proposed by Cakon, Monk and Sun, we
introduce a mixed-element two-grid discretization and prove error estimates for
this method theoretically. Some numerical results are presented to confirm the
theoretical analysis and show that the method here is efficient.
