$\bf H(\mathrm{curl}^2)$ conforming element for Maxwell's transmission eigenvalue problem using fixed-point approach
This work provides a numerical method for computing transmission eigenvalues in electromagnetics, which is important for applications like inverse scattering, but the approach is incremental as it extends existing finite element techniques.
The authors developed H(curl^2) conforming elements to solve Maxwell's transmission eigenvalue problem for both real and complex eigenvalues, achieving optimal error estimates for eigenvalues and eigenfunctions.
Using newly developed ${\bf H}(\mathrm{curl}^2)$ conforming elements, we solve the Maxwell's transmission eigenvalue problem. Both real and complex eigenvalues are considered. Based on the fixed-point weak formulation with reasonable assumptions, the optimal error estimates for numerical eigenvalues and eigenfunctions (in the ${\bf H}(\mathrm{curl}^2)$-norm and ${\bf H}(\mathrm{curl})$-semi-norm) are established.