Document Type
Article
Publication Date
5-13-2022
Department
Department of Mathematical Sciences
Abstract
In this paper, we consider a priori and a posteriori error estimates of the H(curl2)-conforming finite element when solving the quad-curl eigenvalue problem. An a priori estimate of eigenvalues with convergence order 2(s − 1) is obtained if the corresponding eigenvector u ∈ Hs − 1(Ω) and ∇ × u ∈ Hs(Ω). For the a posteriori estimate, by analyzing the associated source problem, we obtain lower and upper bounds for the errors of eigenvectors in the energy norm and upper bounds for the errors of eigenvalues. Numerical examples are presented for validation.
Publication Title
ESAIM: Mathematical Modelling and Numerical Analysis
Recommended Citation
Wang, L.,
Zhang, Q.,
Sun, J.,
&
Zhang, Z.
(2022).
A priori and a posteriori error estimates for the quad-curl eigenvalue problem.
ESAIM: Mathematical Modelling and Numerical Analysis,
56(3), 1027-1051.
http://doi.org/10.1051/m2an/2022027
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/16110
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Version
Publisher's PDF
Publisher's Statement
© The authors. Published by EDP Sciences, SMAI 2022. Publisher’s version of record:
https://doi.org/10.1051/m2an/2022027