| Issue |
ESAIM: M2AN
Volume 56, Number 3, May-June 2022
|
|
|---|---|---|
| Page(s) | 1027 - 1051 | |
| DOI | https://doi.org/10.1051/m2an/2022027 | |
| Published online | 13 May 2022 | |
A priori and a posteriori error estimates for the quad-curl eigenvalue problem
1
School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, P.R. China
2
Beijing Computational Science Research Center, Beijing 100193, P.R. China
3
Department of Mathematical Sciences, Michigan Technological University, Houghton, MI 49931, USA
4
Department of Mathematics, Wayne State University, Detroit, MI 48202, USA
* Corresponding author: qzhang15@mtu.edu
Received:
16
September
2021
Accepted:
10
March
2022
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.
Mathematics Subject Classification: 65N15 / 65N25 / 65N30 / 76W05
Key words: The quad-curl problem / eigenvalue problem / a priori error estimation / a posteriori error estimation / curl-curl conforming elements
© The authors. Published by EDP Sciences, SMAI 2022
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