A priori and a posteriori error estimates for the quad-curl eigenvalue problem

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...

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Bibliographic Details
Published in:arXiv.org 2020-07
Main Authors: Wang, Lixiu, Zhang, Qian, Sun, Jiguang, Zhang, Zhimin
Format: Article
Language:English
Subjects:
Eigenvalues
Eigenvectors
Upper bounds
Online Access:Get full text
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Summary: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.
ISSN:2331-8422