A simple finite element method for the Stokes equations
The goal of this paper is to introduce a simple finite element method to solve the Stokes equations. This method is in primal velocitypressure formulation and is so simple such that both velocity and pressure are approximated by piecewise constant functions. Implementation issues as well as error analysis are investigated. A basis for a divergence free subspace of the velocity field is constructed so that the original saddle point problem can be reduced to a symmetric and positive definite system with much fewer unknowns. The numerical experiments indicate that the method is accurate.
 Authors:

^{[1]}
;
^{[2]}
 Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
 Univ. of Arkansas, Little Rock, AR (United States)
 Publication Date:
 Grant/Contract Number:
 AC0500OR22725
 Type:
 Accepted Manuscript
 Journal Name:
 Advances in Computational Mathematics
 Additional Journal Information:
 Journal Volume: 43; Journal Issue: 6; Journal ID: ISSN 10197168
 Publisher:
 Springer
 Research Org:
 Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
 Sponsoring Org:
 USDOE
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING
 OSTI Identifier:
 1362244
Mu, Lin, and Ye, Xiu. A simple finite element method for the Stokes equations. United States: N. p.,
Web. doi:10.1007/s104440179526z.
Mu, Lin, & Ye, Xiu. A simple finite element method for the Stokes equations. United States. doi:10.1007/s104440179526z.
Mu, Lin, and Ye, Xiu. 2017.
"A simple finite element method for the Stokes equations". United States.
doi:10.1007/s104440179526z. https://www.osti.gov/servlets/purl/1362244.
@article{osti_1362244,
title = {A simple finite element method for the Stokes equations},
author = {Mu, Lin and Ye, Xiu},
abstractNote = {The goal of this paper is to introduce a simple finite element method to solve the Stokes equations. This method is in primal velocitypressure formulation and is so simple such that both velocity and pressure are approximated by piecewise constant functions. Implementation issues as well as error analysis are investigated. A basis for a divergence free subspace of the velocity field is constructed so that the original saddle point problem can be reduced to a symmetric and positive definite system with much fewer unknowns. The numerical experiments indicate that the method is accurate.},
doi = {10.1007/s104440179526z},
journal = {Advances in Computational Mathematics},
number = 6,
volume = 43,
place = {United States},
year = {2017},
month = {3}
}