A C0IPG method and its error estimates for the Helmholtz transmission eigenvalue problem

The interior penalty methods using C0 Lagrange elements (C0IPG) developed in the last decade for the fourth order problems are an interesting topic in academia at present. In this paper, we apply the methods to the Helmholtz transmission eigenvalue problem which is quadratic and non self-adjoint and has important applications in the inverse scattering theory. We propose a discrete scheme, present a complete error analysis and first prove the C0IPG method can capture smooth eigenpairs efficiently. Using the argument in this paper we can prove that the C0IPG methods for the fourth order eigenvalue problems in the existing literature can also capture smooth eigenpairs efficiently. Numerical examples confirm our theoretical analysis.