  The transmission eigenvalue problem is an important and challenging topic
arising in the inverse scattering theory. In this paper, for the Helmholtz
transmission eigenvalue problem, we give a weak formulation which is a
nonselfadjoint linear eigenvalue problem. Based on the weak formulation, we
first discuss the non-conforming finite element approximation, and prove the
error estimates of the discrete eigenvalues obtained by the Adini element,
Morley-Zienkiewicz element, modified-Zienkiewicz element et. al. And we report
some numerical examples to validate the efficiency of our approach for solving
transmission eigenvalue problem.
