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
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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 -