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

Masahisa Tabata, Daisuke Tagami

Research output: Contribution to journalArticle

3 Citations (Scopus)

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 languageEnglish
Pages (from-to)40-57
Number of pages18
JournalSIAM Journal on Numerical Analysis
Volume38
Issue number1
DOIs
Publication statusPublished - 2001

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Surface Tension
Navier Stokes equations
Surface tension
Navier-Stokes Equations
Finite Element
Finite element method
Topology
Second-order Derivatives
Optimal Error Estimates
Solvability
Boundary conditions
Derivatives
Numerical Results
Approximation

All Science Journal Classification (ASJC) codes

  • Numerical Analysis

Cite this

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

In: SIAM Journal on Numerical Analysis, Vol. 38, No. 1, 2001, p. 40-57.

Research output: Contribution to journalArticle

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