论文标题
Quad-Curl特征值问题的先验和后验错误估计
A priori and a posteriori error estimates for the quad-curl eigenvalue problem
论文作者
论文摘要
在本文中，我们提出了一个新的H（curl^2）的新家族，以合并2D中的四曲和特征值问题。该家族的准确性比[32]中高的订单高。我们证明了先验和后验错误估计。如果h^{s+1}（ω）中的特征向量u \，则获得具有收敛顺序2（s-1）特征值的先验估计值。对于A后验估计值，通过分析相关的源问题，我们在能量标准中获得了特征向量的下限和上限，并获得了特征值的上限。提出了数值示例以进行验证。
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}(Ω). 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.
