$H$(${\rm curl}^2$) Conforming Element for Maxwell’s Transmission Eigenvalue Problem Using Fixed-Point Approach (CSIAM Transactions on Applied Mathematics, 2025)
Using newly developed $H$(${\rm curl}^2$) conforming elements, we solve theMaxwell’s transmission eigenvalue problem. Both real and complex eigenvalues areconsidered. Based on the fixed-point weak formulation with reasonable assumptions,the optimal error estimates for numerical eigenvalues and eigenfunctions (in the $H$(${\rm curl}^2$)-norm and $H{\rm (curl)}$-semi-norm) are established. Numerical experiments areperformed to verify the theoretical assumptions and confirm our theoretical analysis.