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Title: A simple finite element method for the Stokes equations

Journal Article · · Advances in Computational Mathematics
ORCiD logo [1];  [2]
  1. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
  2. Univ. of Arkansas, Little Rock, AR (United States)
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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.

Research Organization:
Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
Sponsoring Organization:
USDOE
Grant/Contract Number:
AC05-00OR22725
OSTI ID:
1362244
Journal Information:
Advances in Computational Mathematics, Vol. 43, Issue 6; ISSN 1019-7168
Publisher:
SpringerCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 6 works
Citation information provided by
Web of Science

References (6)

Computers & Fluids: Aims and Objectives journal January 1973
A Robust Numerical Method for Stokes Equations Based on Divergence-Free H (div) Finite Element Methods journal January 2009
A weak Galerkin finite element method for second-order elliptic problems journal March 2013
A weak Galerkin mixed finite element method for second order elliptic problems journal May 2014
The construction of a null basis for a discrete divergence operator journal March 1995
Stabilized discontinuous finite element approximations for Stokes equations journal January 2007

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Related Subjects

97 MATHEMATICS AND COMPUTING