<i>A priori</i> and <i>a posteriori</i> error estimates for the quad-curl eigenvalue problem

Wang, Lixiu; Zhang, Qian; Sun, Jiguang; Zhang, Zhimin

doi:10.1051/m2an/2022027

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

Wang, Lixiu ; Zhang, Qian ; Sun, Jiguang ; Zhang, Zhimin

ESAIM: Mathematical Modelling and Numerical Analysis , Tome 56 (2022) no. 3, pp. 1027-1051

Résumé

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 $$ ∈ $$$$(Ω) and ∇ × $$ ∈ $$$$(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.

MR

DOI : 10.1051/m2an/2022027

Classification : 65N15, 65N25, 65N30, 76W05
Keywords: The quad-curl problem, eigenvalue problem, $$ error estimation, $$ error estimation, curl-curl conforming elements

@article{M2AN_2022__56_3_1027_0,
     author = {Wang, Lixiu and Zhang, Qian and Sun, Jiguang and Zhang, Zhimin},
     title = {\protect\emph{A priori} and \protect\emph{a posteriori} error estimates for the quad-curl eigenvalue problem},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {1027--1051},
     year = {2022},
     publisher = {EDP-Sciences},
     volume = {56},
     number = {3},
     doi = {10.1051/m2an/2022027},
     mrnumber = {4420892},
     language = {en},
     url = {https://www.numdam.org/articles/10.1051/m2an/2022027/}
}

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Wang, Lixiu; Zhang, Qian; Sun, Jiguang; Zhang, Zhimin. A priori and a posteriori error estimates for the quad-curl eigenvalue problem. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 56 (2022) no. 3, pp. 1027-1051. doi: 10.1051/m2an/2022027

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