Mixed methods for the elastic transmission eigenvalue problem

摘要

The elastic transmission eigenvalue problem is quadratic in the eigenvalue parameter, nonselfadjoint, and of fourth order. In this paper, we apply the Ciarlet–Raviart mixed method to this problem, give a mixed variational form, and establish two mixed methods using the classical Lagrange finite element and the spectral element, respectively. We deduce the error estimates of the discrete eigenpairs. Theoretical analysis and numerical experiments show that these two methods are simple and easy to implement, and can efficiently compute real and complex elastic transmission eigenvalues.