A Holomorphic Operator Function Approach for the Modified Transmission Eigenvalue Problem

The paper presents a holomorphic operator function approach for solving the modified transmission eigenvalue problem using the finite element method. To use the abstract approximation theory for holomorphic operator functions, we rewrite the modified transmission eigenvalue problem as the eigenvalue problem of a holomorphic Fredholm operator function of index zero. The convergence of the finite element method is proved following the abstract theory of the holomorphic Fredholm operator function. Numerical examples are presented to validate the theory.