A two-grid method of the non-conforming Crouzeix-Raviart element for the Steklov eigenvalue problem
A two-grid method of the non-conforming Crouzeix-Raviart element for the Steklov eigenvalue problem
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DOI：
10.1016/j.amc.2011.04.051
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发表时间：
2011-08
期刊：
影响因子：
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通讯作者：
H. Bi;Yidu Yang
中科院分区：
文献类型：
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作者：
H. Bi;Yidu Yang
本文讨论了Steklov特征值问题的一种高效格式。建立了一种两层网格的Crouzeix-Raviart单元离散格式。利用这种格式，在细网格π h上求解Steklov特征值问题可化为在粗网格π H上求解特征值问题和在细网格π h上求解线性代数方程组.利用谱逼近理论和Nitsche-Lascaux-Lesaint技巧，在H-12（Ω）空间中，证明了当H= h时，用我们的方法得到的解能保持渐近最优精度.数值实验表明，当λ k，h从下而上逼近精确特征值时，两网格离散格式得到的近似特征值λ k，h从下而上也逼近精确特征值，且λ k，h的精度高于λ k，h。
This paper discusses a high efficient scheme for the Steklov eigenvalue problem. A two-grid discretization scheme of nonconforming Crouzeix–Raviart element is established. With this scheme, the solution of a Steklov eigenvalue problem on a fine grid π h is reduced to the solution of the eigenvalue problem on a much coarser grid π H and the solution of a linear algebraic system on the fine grid π h. By using spectral approximation theory and Nitsche–Lascaux–Lesaint technique in space H-1 2 (∂ Ω), we prove that the resulting solution obtained by our scheme can maintain an asymptotically optimal accuracy by taking H= h. And the numerical experiments indicate that when the eigenvalues λ k, h of nonconforming Crouzeix–Raviart element approximate the exact eigenvalues from below, the approximate eigenvalues λ k, h∗ obtained by the two-grid discretization scheme also approximate the exact ones from below, and the accuracy of λ k, h∗ is higher than that of λ k, h.