H(curl²) Conforming Element for Maxwell's Transmission Eigenvalue Problem Using Fixed-Point Approach

Abstract

Using newly developed $\mathbf{H}$ (curl²) 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 $\mathbf{H}$ (curl²)-norm and $\mathbf{H}$ (curl)-semi-norm) are established. Numerical experiments are performed to verify the theoretical assumptions and confirm our theoretical analysis.

Keywords

Maxwell's transmission eigenvalues / curl-curl conforming element / error estimates