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.

中文翻译：

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四卷曲特征值问题的先验和后验误差估计

在本文中，我们为二维四边形卷曲特征值问题提出了一个新的符合 H(curl^2) 的元素族。该系列的准确度比 [32] 中的高一个数量级。我们证明了先验和后验误差估计。如果特征向量 u\in H^{s+1}(Ω)，则获得收敛阶数为 2(s-1) 的特征值的先验估计。对于后验估计，通过分析相关的源问题，我们获得能量范数中特征向量的下限和上限以及特征值的上限。提供了数值示例以供验证。