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Asymptotic lower bounds for eigenvalues of the Steklov eigenvalue problem with variable coefficients
Applications of Mathematics ( IF 0.6 ) Pub Date : 2020-09-09 , DOI: 10.21136/am.2020.0108-19
Yu Zhang , Hai Bi , Yidu Yang

In this paper, using new correction to the Crouzeix-Raviart finite element eigenvalue approximations, we obtain lower eigenvalue bounds for the Steklov eigenvalue problem with variable coefficients on d-dimensional domains (d = 2,3). In addition, we prove that the corrected eigenvalues asymptotically converge to the exact ones from below whether the eigenfunctions are singular or smooth and whether the eigenvalues are large enough or not. Further, we prove that the corrected eigenvalues still maintain the same convergence order as that of uncorrected eigenvalues. Finally, numerical experiments validate our theoretical results.

中文翻译:

具有可变系数的 Steklov 特征值问题的特征值的渐近下界

在本文中,使用对 Crouzeix-Raviart 有限元特征值近似的新修正,我们获得了 Steklov 特征值问题的特征值下限,在 d 维域 (d = 2,3) 上具有可变系数。此外,我们证明了无论特征函数是奇异的还是平滑的,特征值是否足够大,校正后的特征值从下方渐近收敛到精确的特征值。此外,我们证明校正后的特征值仍然保持与未校正特征值相同的收敛顺序。最后,数值实验验证了我们的理论结果。
更新日期:2020-09-09
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