### Abstract

Error estimates are obtained for finite element approximations of the drag and the lift of a body immersed in nonstationary Navier-Stokes flows. By virtue of a consistent flux technique, the error estimates are reduced to those of the velocity as well as its first order derivatives and the pressure. Semi-implicit backward Euler method is used for the time integration and no stability condition is required. The error estimate in a square summation norm is optimal in the sense that it has the same order as the fundamental error estimate of the velocity. The error estimate in the supremum norm is not optimal in general but it is so for some finite elements.

Original language | English |
---|---|

Pages (from-to) | 371-389 |

Number of pages | 19 |

Journal | Japan Journal of Industrial and Applied Mathematics |

Volume | 17 |

Issue number | 3 |

Publication status | Published - 2000 Oct |

Externally published | Yes |

### Fingerprint

### Keywords

- Drag and lift
- Error estimates
- Finite element method
- Nonstationary Navier-Stokes equations

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Japan Journal of Industrial and Applied Mathematics*,

*17*(3), 371-389.

**Error Estimates for Finite Element Approximations of Drag and Lift in Nonstationary Navier-Stokes Flows.** / Tabata, Masahisa; Tagami, Daisuke.

Research output: Contribution to journal › Article

*Japan Journal of Industrial and Applied Mathematics*, vol. 17, no. 3, pp. 371-389.

}

TY - JOUR

T1 - Error Estimates for Finite Element Approximations of Drag and Lift in Nonstationary Navier-Stokes Flows

AU - Tabata, Masahisa

AU - Tagami, Daisuke

PY - 2000/10

Y1 - 2000/10

N2 - Error estimates are obtained for finite element approximations of the drag and the lift of a body immersed in nonstationary Navier-Stokes flows. By virtue of a consistent flux technique, the error estimates are reduced to those of the velocity as well as its first order derivatives and the pressure. Semi-implicit backward Euler method is used for the time integration and no stability condition is required. The error estimate in a square summation norm is optimal in the sense that it has the same order as the fundamental error estimate of the velocity. The error estimate in the supremum norm is not optimal in general but it is so for some finite elements.

AB - Error estimates are obtained for finite element approximations of the drag and the lift of a body immersed in nonstationary Navier-Stokes flows. By virtue of a consistent flux technique, the error estimates are reduced to those of the velocity as well as its first order derivatives and the pressure. Semi-implicit backward Euler method is used for the time integration and no stability condition is required. The error estimate in a square summation norm is optimal in the sense that it has the same order as the fundamental error estimate of the velocity. The error estimate in the supremum norm is not optimal in general but it is so for some finite elements.

KW - Drag and lift

KW - Error estimates

KW - Finite element method

KW - Nonstationary Navier-Stokes equations

UR - http://www.scopus.com/inward/record.url?scp=0346356089&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0346356089&partnerID=8YFLogxK

M3 - Article

VL - 17

SP - 371

EP - 389

JO - Japan Journal of Industrial and Applied Mathematics

JF - Japan Journal of Industrial and Applied Mathematics

SN - 0916-7005

IS - 3

ER -