The aim of the present work is to derive error estimates for the Laplace eigenvalue problem in mixed form, implementing a virtual element method. With the aid of the theory for non-compact operators, we prove that the proposed method is spurious free and convergent. Optimal order of convergence for the eigenvalues and eigenfunctions are derived. Finally, we report numerical tests to confirm the theoretical results together with a rigorous computational analysis of the effects of the stabilization parameter, inherent for the virtual element methods, in the computation of the spectrum.

中文翻译：

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拉普拉斯算子的频谱问题的混合VEM离散化的先验误差分析

本工作的目的是以混合形式导出拉普拉斯特征值问题的误差估计，并实现虚拟元素方法。借助非紧致算符的理论，我们证明了所提出的方法是无杂散且收敛的。推导了特征值和特征函数的最优收敛顺序。最后，我们报告了数值测试，以确认理论结果以及对稳定元素的影响的严格计算分析，这是虚拟元素方法固有的在频谱计算中的作用。