《工程》是中国工程院(CAE)于2015年推出的国际开放存取期刊。其目的是提供一个高水平的平台,传播和分享工程研发的前沿进展、当前主要研究成果和关键成果;报告工程科学的进展,讨论工程发展的热点、兴趣领域、挑战和前景,在工程中考虑人与环境的福祉和伦理道德,鼓励具有深远经济和社会意义的工程突破和创新,使之达到国际先进水平,成为新的生产力,从而改变世界,造福人类,创造新的未来。 期刊链接:https://www.sciencedirect.com/journal/engineering

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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 1.5, 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.

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