TY - JOUR
T1 - $\mathbf{H}$(${\rm curl}^2$) Conforming Element for Maxwell’s Transmission Eigenvalue Problem Using Fixed-Point Approach
AU - Han , Jiayu
AU - Zhang , Zhimin
JO - CSIAM Transactions on Applied Mathematics
VL - 3
SP - 468
EP - 488
PY - 2025
DA - 2025/09
SN - 6
DO - http://doi.org/10.4208/csiam-am.SO-2021-0046
UR - https://global-sci.org/intro/article_detail/csiam-am/24372.html
KW - Maxwell’s transmission eigenvalues, curl-curl conforming element, error estimates.
AB - <p style="text-align: justify;">Using newly developed $\mathbf{H}$(${\rm curl}^2$) 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&nbsp;<span style="text-align: justify; text-wrap-mode: wrap;">$\mathbf{H}$(${\rm curl}^2$)</span>-norm and $\mathbf{H}{\rm (curl)}$-semi-norm) are established. Numerical experiments are
performed to verify the theoretical assumptions and confirm our theoretical analysis.</p>