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Volume 6, Issue 3
$\mathbf{H}$(${\rm curl}^2$) Conforming Element for Maxwell’s Transmission Eigenvalue Problem Using Fixed-Point Approach

Jiayu Han & Zhimin Zhang

DOI: 10.4208/csiam-am.SO-2021-0046

CSIAM Trans. Appl. Math., 6 (2025), pp. 468-488.

Published online: 2025-09

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  • Abstract

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 $\mathbf{H}$(${\rm curl}^2$)-norm and $\mathbf{H}{\rm (curl)}$-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.

  • AMS Subject Headings

65N25, 65N30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CSIAM-AM-6-468, author = {Han , Jiayu and Zhang , Zhimin}, title = {$\mathbf{H}$(${\rm curl}^2$) Conforming Element for Maxwell’s Transmission Eigenvalue Problem Using Fixed-Point Approach}, journal = {CSIAM Transactions on Applied Mathematics}, year = {2025}, volume = {6}, number = {3}, pages = {468--488}, abstract = {

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 $\mathbf{H}$(${\rm curl}^2$)-norm and $\mathbf{H}{\rm (curl)}$-semi-norm) are established. Numerical experiments are performed to verify the theoretical assumptions and confirm our theoretical analysis.

}, issn = {2708-0579}, doi = {https://doi.org/10.4208/csiam-am.SO-2021-0046}, url = {http://global-sci.org/intro/article_detail/csiam-am/24372.html} }
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 -

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 $\mathbf{H}$(${\rm curl}^2$)-norm and $\mathbf{H}{\rm (curl)}$-semi-norm) are established. Numerical experiments are performed to verify the theoretical assumptions and confirm our theoretical analysis.

Han , Jiayu and Zhang , Zhimin. (2025). $\mathbf{H}$(${\rm curl}^2$) Conforming Element for Maxwell’s Transmission Eigenvalue Problem Using Fixed-Point Approach. CSIAM Transactions on Applied Mathematics. 6 (3). 468-488. doi:10.4208/csiam-am.SO-2021-0046
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