Discontinuous Galerkin methods of the non-selfadjoint Steklov eigenvalue problem in inverse scattering

In this paper, we apply discontinuous Galerkin methods to the non-selfadjoint Steklov eigenvalue problem arising in inverse scattering. The variational formulation of the problem is non-selfadjoint and does not satisfy H¹-elliptic condition. By using the spectral approximation theory of compact operators, we prove the spectral approximation and optimal convergence order for the eigenvalues. Finally, some numerical experiments are reported to show that the proposed numerical schemes are efficient for real and complex Steklov eigenvalues.