### Abstract

A finite element analysis is performed for a stationary linearized problem of the Navier-Stokes equations with surface tension. Since the surface tension brings about a second-order derivative of the velocity in the boundary condition, the velocity space is equipped with a stronger topology than in the conventional case. Under the strong topology, conditions of the uniform solvability and the approximation are verified on some pairs of finite element spaces for the velocity and the pressure. Thus an optimal error estimate is derived. Some numerical results are shown, which agree well with theoretical ones.

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

Pages (from-to) | 40-57 |

Number of pages | 18 |

Journal | SIAM Journal on Numerical Analysis |

Volume | 38 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2001 |

Externally published | Yes |

### Fingerprint

### Keywords

- Finite element methods
- Inf-sup condition
- Navier-Stokes equations
- Optimal error estimates
- Surface tension

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics
- Computational Mathematics

### Cite this

*SIAM Journal on Numerical Analysis*,

*38*(1), 40-57. https://doi.org/10.1137/S0036142997329098

**A finite element analysis of a linearized problem of the Navier-Stokes equations with surface tension.** / Tabata, Masahisa; Tagami, Daisuke.

Research output: Contribution to journal › Article

*SIAM Journal on Numerical Analysis*, vol. 38, no. 1, pp. 40-57. https://doi.org/10.1137/S0036142997329098

}

TY - JOUR

T1 - A finite element analysis of a linearized problem of the Navier-Stokes equations with surface tension

AU - Tabata, Masahisa

AU - Tagami, Daisuke

PY - 2001

Y1 - 2001

N2 - A finite element analysis is performed for a stationary linearized problem of the Navier-Stokes equations with surface tension. Since the surface tension brings about a second-order derivative of the velocity in the boundary condition, the velocity space is equipped with a stronger topology than in the conventional case. Under the strong topology, conditions of the uniform solvability and the approximation are verified on some pairs of finite element spaces for the velocity and the pressure. Thus an optimal error estimate is derived. Some numerical results are shown, which agree well with theoretical ones.

AB - A finite element analysis is performed for a stationary linearized problem of the Navier-Stokes equations with surface tension. Since the surface tension brings about a second-order derivative of the velocity in the boundary condition, the velocity space is equipped with a stronger topology than in the conventional case. Under the strong topology, conditions of the uniform solvability and the approximation are verified on some pairs of finite element spaces for the velocity and the pressure. Thus an optimal error estimate is derived. Some numerical results are shown, which agree well with theoretical ones.

KW - Finite element methods

KW - Inf-sup condition

KW - Navier-Stokes equations

KW - Optimal error estimates

KW - Surface tension

UR - http://www.scopus.com/inward/record.url?scp=0041692598&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0041692598&partnerID=8YFLogxK

U2 - 10.1137/S0036142997329098

DO - 10.1137/S0036142997329098

M3 - Article

AN - SCOPUS:0041692598

VL - 38

SP - 40

EP - 57

JO - SIAM Journal on Numerical Analysis

JF - SIAM Journal on Numerical Analysis

SN - 0036-1429

IS - 1

ER -