In two and three dimensional domains, we analyze mixed finite element methods for a velocity-pressure-pseudostress formulation of the Stokes eigenvalue problem. The methods consist in two schemes: the velocity and pressure are approximated with piecewise polynomial and for the pseudostress we consider two classic families of finite elements for $\mathrm{H}(\mathop{\mathrm{div}})$ spaces: the Raviart-Thomas and the Brezzi-Douglas Marini elements. With the aid of the classic spectral theory for compact operators, we prove that our method does not introduce spurious modes. Also, we obtain convergence and error estimates for the proposed methods. In order to assess the performance of the schemes, we report numerical results to compare the accuracy and robustness between both numerical schemes.

翻译：在二维和三维域中,我们分析用于Stokes egenvalue问题速度压力-假模模模数配制的混合限量元素方法。方法包括两种方案:速度和压力近似于片面多面体;假施压者,我们考虑用美元/马特尔姆(H})(\mathop_mathrm{div ⁇ )为两个典型的有限元素组合,即:Raviart-Thomas和Brezzi-Douglas Marini元素。在传统光谱理论的帮助下,我们证明我们的方法没有引入虚假的模式。此外,我们获得了拟议方法的趋同和误差估计。为了评估这些方法的性能,我们报告数字结果,以比较两个数字方法的准确性和稳健性。