Superconvergence of the MINI mixed finite element discretization of the Stokes problem: An experimental study in 3D

Stokes flows are a type of fluid flow where convective forces small in comparison with viscous forces, and momentum transport is entirely due to diffusion. Besides being routinely used as benchmark test cases numerical dynamics, relevant several applications science engineering including porous media flow, biological flows, microfluidics, microrobotics, hydrodynamic lubrication. The present study concerns the discretization equations motion three dimensions utilizing MINI mixed finite element, focusing on superconvergence method which was investigated experiments using five purpose-made analytical solution. Despite fact that element only linearly convergent according standard theory, recent theoretical development proves that, for structured meshes two dimensions, pressure superconverges order O(h3/2), well linear part computed velocity respect piecewise-linear nodal interpolation exact velocity. documented herein suggest more general validity pressure, possibly unstructured tetrahedral even up quadratic convergence observed one problem, thereby indicating there scope further extend available results convergence.