Work

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

Year: 2025

Type: article

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.

Source: CSIAM Transactions on Applied Mathematics

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

Authors: Jiayu Han, Zhimin Zhang

Institutions: Guizhou Normal University, Wayne State University

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: diamond

Funders: National Natural Science Foundation of China, China Postdoctoral Science Foundation, Guizhou Science and Technology Department, National Safety Academic Fund