298 IGPM298.pdf        March 2009
TITLE Nitsche's Method for a Transport Problem in Two-Phase Incompressible Flows
AUTHORS Arnold Reusken, Trung Hieu Nguyen
ABSTRACT We consider a parabolic interface problem which models the transport of a dissolved species in two-phase incompressible flow problems. Due to the so-called Henry interface condition the solution is discontinuous across the interface. We use an extended finite element space combined with a method due to Nitsche for the spatial discretization of this problem and derive optimal discretization error bounds for this method. For the time discretization a standard θ-scheme is applied. Results of numerical experiments are given that illustrate the convergence properties of this discretization.
KEYWORDS Nitsche’s method, interface problem, extended finite elements, two-phase flows,
DOI 10.1007/s00041-009-9092-y
PUBLICATION The journal of Fourier analysis and applications
15(5), 663-683 (2009)