$\mathbf{H}({\mathrm{curl}}^2)$ conforming element for Maxwell's transmission eigenvalue problem using fixed-point approach

Abstract

Using newly developed $\mathbf{H}({\mathrm{curl}}^2)$ 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 $\mathbf{H}({\mathrm{curl}}^2)$-norm and $\mathbf{H}(\mathrm{curl})$-semi-norm) are established.