A priori and a posteriori error estimates for the quad-curl eigenvalue problem
Numerical Analysis
2020-07-06 v1 Numerical Analysis
Abstract
In this paper, we propose a new family of H(curl^2)-conforming elements for the quad-curl eigenvalue problem in 2D. The accuracy of this family is one order higher than that in [32]. We prove a priori and a posteriori error estimates. The a priori estimate of the eigenvalue with a convergence order 2(s-1) is obtained if the eigenvector u\in H^{s+1}(\Omega). For the a posteriori estimate, by analyzing the associated source problem, we obtain lower and upper bounds for the eigenvector in an energy norm and an upper bound for the eigenvalues. Numerical examples are presented for validation.
Cite
@article{arxiv.2007.01330,
title = {A priori and a posteriori error estimates for the quad-curl eigenvalue problem},
author = {Lixiu Wang and Qian Zhang and Jiguang Sun and Zhimin Zhang},
journal= {arXiv preprint arXiv:2007.01330},
year = {2020}
}
Comments
26 pages, 9 figures