In this paper, we consider a stabilized finite element method for the approximation of the Stokes eigenvalue problem on triangular domains. The method depends on orthogonal subscales that has proved to be an appropriate means for approximating eigenvalue problems in the framework of residual based approaches. We consider several isosceles triangular domains with various apex angles to investigate the characteristics of the eigensolutions in regards to the variation of the domain properties. This study presents the first finite element approximation to the solutions of the Stokes eigenvalue problem on triangular domains, to the best of our knowledge. We provide plots of several velocity and pressure fields corresponding to the fundamental eigenmodes to analyze the flow characteristics in detail. Furthermore, we consider the problem on triangular domains including a crack, and investigate the influence of the length of the slit on the fundamental mode to some extent. The results reveal the correlation between the domain properties and the eigenpairs, and the fact that there are various critical lengths of the slit where the eigenspace is notably affected.

在本文中，我们考虑了一种稳定的有限元方法来近似三角区域上的斯托克斯特征值问题。该方法依赖于正交子尺度，该子尺度已被证明是在基于残差的方法框架中逼近特征值问题的合适方法。我们考虑了几个具有不同顶角的等腰三角形畴，以研究关于本征性质变化的本征解的特征。据我们所知，本研究提出了三角形域上斯托克斯特征值问题解的第一个有限元逼近。我们提供了一些与基本本征模式相对应的速度场和压力场的图，以详细分析流动特性。此外，我们考虑了包括裂纹在内的三角形区域的问题，并在一定程度上研究了缝隙长度对基本模式的影响。结果揭示了域特性与本征对之间的相关性，以及在本征空间受到显着影响的狭缝的各种临界长度这一事实。