380 IGPM.pdf        January 2014
TITLE Finite Element Discretization Error Analysis of a General Interfacial Stress Functional
AUTHORS Jörg Grande
KEYWORDS two phase flow, variable interfacial tension, interfacial stress tensor, finite elements
PUBLICATION A stationary, incompressible two-phase flow problem with a variable interfacial stress tensor σΓ (x) is considered. Variable interfacial tension is included as a special case. In the weak formulation, the interfacial stress gives rise to a functional which is supported on the interface Γ. A new finite element discretization of this functional is presented and analyzed. The discretization admits almost independent meshes for the approximation of the interface and the approximation of the flow variables. The main result is an O(h,k+1/2 )-error-bound in a natural norm, if the discrete interface is an O(hk+1) -approximation of Γ. The bound is shown to be sharp in a numerical experiment.