C⁰ IP Methods for the Transmission Eigenvalue Problem

We consider a non-selfadjoint fourth order eigenvalue problem using a discontinuous Galerkin (DG) method. For high order problems, DG methods are competitive since they use simple basis functions and have less degrees of freedom. The numerical implementation is much easier compared with classical conforming finite element methods. In this paper, we propose an interior penalty discontinuous Galerkin method using C⁰ Lagrange elements (C⁰IP) for the transmission eigenvalue problem and prove the optimal convergence. The method is applied to several examples and its effectiveness is validated.