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

10/27/2021
by   Andrea Cioncolini, et al.
0

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.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 15

08/05/2019

A new unified stabilized mixed finite element method of the Stokes-Darcy coupled problem: Isotropic discretization

In this paper we develop an a priori error analysis of a new unified mix...
02/27/2020

A nonconforming pressure-robust finite element method for the Stokes equations on anisotropic meshes

Most classical finite element schemes for the (Navier-)Stokes equations ...
07/22/2019

Numerical analysis of a projection-based stabilized POD-ROM for incompressible flows

In this paper, we propose a new stabilized projection-based POD-ROM for ...
01/19/2021

Combined Newton-Raphson and Streamlines-Upwind Petrov-Galerkin iterations for nano-particles transport in buoyancy driven flow

The present study deals with the finite element discretization of nanofl...
05/06/2020

Optimally Convergent Mixed Finite Element Methods for the Stochastic Stokes Equations

We propose some new mixed finite element methods for the time dependent ...
06/01/2021

A reduced 3D-0D FSI model of the aortic valve including leaflets curvature

In the present work, we propose a novel lumped-parameter model for the d...
03/04/2021

A vertex scheme for two-phase flow in heterogeneous media

This paper presents the numerical solution of immiscible two-phase flows...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.