262 IGPM262.pdf        August 2006
TITLE Finite Element Discretization Error Analysis of a Surface Tension Force in Two-Phase Incompressible Flows
AUTHORS Sven Groß, Arnold Reusken
ABSTRACT We consider a standard model for a stationary two-phase incompressible flow with surface tension. In the variational formulation of the model a linear functional which describes the surface tension force occurs. This functional depends on the location and the curvature of the (unknown) interface. In a finite element discretization method the functional has to be approximated. For an approximation method based on a Laplace-Beltrami representation of the curvature we derive sharp bounds for the approximation error. A new modified approximation method with a significantly smaller error is introduced.
KEYWORDS two-phase flow, continuum surface force technique, interface, Laplace–Beltrami operator, finite elements
DOI 10.1137/060667530
PUBLICATION SIAM journal on numerical analysis
45(4), 1679-1700 (2007)