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Title: 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 velocity-pressure 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:
ORCiD logo [1] ;  [2]
  1. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
  2. Univ. of Arkansas, Little Rock, AR (United States)
Publication Date:
Grant/Contract Number:
AC05-00OR22725
Type:
Accepted Manuscript
Journal Name:
Advances in Computational Mathematics
Additional Journal Information:
Journal Volume: 43; Journal Issue: 6; Journal ID: ISSN 1019-7168
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/s10444-017-9526-z.
Mu, Lin, & Ye, Xiu. A simple finite element method for the Stokes equations. United States. doi:10.1007/s10444-017-9526-z.
Mu, Lin, and Ye, Xiu. 2017. "A simple finite element method for the Stokes equations". United States. doi:10.1007/s10444-017-9526-z. 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 velocity-pressure 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/s10444-017-9526-z},
journal = {Advances in Computational Mathematics},
number = 6,
volume = 43,
place = {United States},
year = {2017},
month = {3}
}