A C⁰IP method of transmission eigenvalues for elastic waves

This paper develops a discontinuous Galerkin method to compute a few smallest elasticity transmission eigenvalues, which are of practical importance in inverse elastic scattering theory. For high-order problems, comparing with classical conforming finite element methods, discontinuous Galerkin methods use simpler basis functions which make the numerical implementation much easier. In this paper, we propose an interior penalty discontinuous Galerkin method using C⁰ Lagrange elements (C⁰IP) for the elastic transmission eigenvalue problem and prove the optimal convergence. Numerical examples are presented to validate its effectiveness. Both real and complex eigenvalues can be obtained.