# A simple finite element method for the Stokes equations

## Abstract

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:

- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
- Univ. of Arkansas, Little Rock, AR (United States)

- Publication Date:

- Research Org.:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1362244

- Grant/Contract Number:
- AC05-00OR22725

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Advances in Computational Mathematics

- Additional Journal Information:
- Journal Volume: 43; Journal Issue: 6; Journal ID: ISSN 1019-7168

- Publisher:
- Springer

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS AND COMPUTING

### Citation Formats

```
Mu, Lin, and Ye, Xiu.
```*A simple finite element method for the Stokes equations*. United States: N. p., 2017.
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. Tue .
"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 = {Tue Mar 21 00:00:00 EDT 2017},

month = {Tue Mar 21 00:00:00 EDT 2017}

}

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