In this paper, we study the performance of the non-conforming least-squares spectral element method for Stokes problem. Generalized Stokes problem has been considered and the method is shown to be exponential accurate. The numerical method is nonconforming and higher order spectral element functions are used. The same order spectral element functions are used for both velocity and pressure variables. The normal equations in the least-squares formulation are solved efficiently using preconditioned conjugate gradient method. Various test cases are considered including the Stokes problem on curvilinear domains, Stokes problem with mixed boundary conditions and a generalized stokes problem in \mathbb{R}^{3} to verify the accuracy of the method.

翻译：在本文中, 我们研究Stokes 问题的不兼容最小方块光谱元件方法的性能。 普遍化的Stokes 问题已经得到考虑, 且该方法被显示为指数精确。 数字方法不兼容, 并且使用更高的顺序光谱元件功能。 同一顺序光谱元件功能用于速度变量和压力变量。 最小方块配方的正常方程式使用先决条件的同流梯度方法得到了有效解决。 各种测试案例都得到了考虑, 包括曲线域的Stoks 问题、 混合边界条件的Stokes 问题和\ mathbb{R} 中的普遍的斯托克斯 问题, 以核实方法的准确性 。