### Abstract

Viscous splitting algorithms are the underlying design principle for many numerical algorithms which solve the Navier-Stokes equations at high Reynolds number. In this work, error estimates for splitting algorithms are developed which are uniform in the viscosity v as it becomes small for either two- or three-dimensional fluid flow in all of space. In particular, it is proved that standard viscous splitting converges uniformly at the rate CvAt, Strang-type splitting converges at the rate 0(A

Original language | English (US) |
---|---|

Pages (from-to) | 951-958 |

Number of pages | 8 |

Journal | Mathematics of Computation |

Volume | 37 |

Issue number | 156 |

DOIs | |

State | Published - 1981 |

### Fingerprint

### Keywords

- Eulers equations
- Navier-Stokes equations
- Splitting algorithms

### ASJC Scopus subject areas

- Algebra and Number Theory
- Computational Mathematics
- Applied Mathematics

### Cite this

*Mathematics of Computation*,

*37*(156), 951-958. https://doi.org/10.1090/S0025-5718-1981-0628693-0

**Rates of convergence for viscous splitting of the navier stokes equations.** / Thomas Beale, J.; Majda, Andrew.

Research output: Contribution to journal › Article

*Mathematics of Computation*, vol. 37, no. 156, pp. 951-958. https://doi.org/10.1090/S0025-5718-1981-0628693-0

}

TY - JOUR

T1 - Rates of convergence for viscous splitting of the navier stokes equations

AU - Thomas Beale, J.

AU - Majda, Andrew

PY - 1981

Y1 - 1981

N2 - Viscous splitting algorithms are the underlying design principle for many numerical algorithms which solve the Navier-Stokes equations at high Reynolds number. In this work, error estimates for splitting algorithms are developed which are uniform in the viscosity v as it becomes small for either two- or three-dimensional fluid flow in all of space. In particular, it is proved that standard viscous splitting converges uniformly at the rate CvAt, Strang-type splitting converges at the rate 0(A

AB - Viscous splitting algorithms are the underlying design principle for many numerical algorithms which solve the Navier-Stokes equations at high Reynolds number. In this work, error estimates for splitting algorithms are developed which are uniform in the viscosity v as it becomes small for either two- or three-dimensional fluid flow in all of space. In particular, it is proved that standard viscous splitting converges uniformly at the rate CvAt, Strang-type splitting converges at the rate 0(A

KW - Eulers equations

KW - Navier-Stokes equations

KW - Splitting algorithms

UR - http://www.scopus.com/inward/record.url?scp=84966236685&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84966236685&partnerID=8YFLogxK

U2 - 10.1090/S0025-5718-1981-0628693-0

DO - 10.1090/S0025-5718-1981-0628693-0

M3 - Article

VL - 37

SP - 951

EP - 958

JO - Mathematics of Computation

JF - Mathematics of Computation

SN - 0025-5718

IS - 156

ER -