In this paper, we obtain guaranteed lower bounds for eigenvalues of two spectral problems arising in fluid mechanics by using the min–max principles of weak form that can be derived by the principles of operator forms. These two problems are the Laplace model for fluid–solid vibrations and the sloshing problem. We deal with the positive semi-definiteness of the associated bilinear forms by adding some constraints to the solution and finite element spaces. Numerical experiments are reported finally to validate our theoretical results.

中文翻译：

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保证流体力学中出现的两个光谱问题的特征值下界

在本文中，我们通过使用可以由算子形式原理导出的弱形式的最小-最大原理，来获得流体力学中出现的两个光谱问题的特征值的有保证的下界。这两个问题是流体-固体振动的拉普拉斯模型和晃动问题。通过对解和有限元空间添加一些约束，我们处理了相关双线性形式的正半定性。最后报道了数值实验，以验证我们的理论结果。