A finite element method for Maxwell's transmission eigenvalue problem in anisotropic media

In this paper, we introduce a finite element method employing the Ned\'el\'ec element space for solving the Maxwell's transmission eigenvalue problem in anisotropic media. The well-posedness of the source problems are derived using $\mathbb T$-coercivity approach. We discuss the discrete compactness property of the finite element space under the case of anisotropic coefficients and conduct a finite element error analysis for the proposed approach. Additionally, we present some numerical examples to support the theoretical result.