Stokes flows are a type of fluid flow where convective forces are small in comparison with viscous forces, and momentum transport is entirely due to viscous diffusion. Besides being routinely used as benchmark test cases in numerical fluid dynamics, Stokes flows are relevant in several applications in science and engineering including porous media flow, biological flows, microfluidics, microrobotics, and hydrodynamic lubrication. The present study concerns the discretization of the equations of motion of Stokes flows in three dimensions utilizing the MINI mixed finite element, focusing on the superconvergence of the method which was investigated with numerical experiments using five purpose-made benchmark test cases with analytical solution. Despite the fact that the MINI element is only linearly convergent according to standard mixed finite element theory, a recent theoretical development proves that, for structured meshes in two dimensions, the pressure superconverges with order $O\left(h^{3/2}\right)$, as well as the linear part of the computed velocity with respect to the piecewise-linear nodal interpolation of the exact velocity. The numerical experiments documented herein suggest a more general validity of the superconvergence in pressure, possibly to unstructured tetrahedral meshes and even up to quadratic convergence which was observed with one test problem, thereby indicating that there is scope to further extend the available theoretical results on convergence.

斯托克斯流是一种流体流动，与粘性力相比，对流力很小，动量传递完全是由于粘性扩散。除了通常用作数值流体动力学的基准测试案例外，斯托克斯流还与科学和工程中的多种应用相关，包括多孔介质流、生物流、微流体、微型机器人和流体动力润滑。本研究涉及利用 MINI 混合有限元在三个维度上离散化斯托克斯流的运动方程，重点是该方法的超收敛性，该方法通过数值实验进行了研究，使用五个具有解析解的专用基准测试案例。$哦\left(H^{3/2}\right)$，以及相对于精确速度的分段线性节点插值计算速度的线性部分。此处记录的数值实验表明压力超收敛的更普遍有效性，可能适用于非结构化四面体网格，甚至可以达到用一个测试问题观察到的二次收敛，从而表明有进一步扩展可用的收敛理论结果的空间.