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.
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Communicated by Stephan Dahlke.
Dedicated to Wolfgang Dahmen on the occasion of his 60th birthday.
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Reusken, A., Nguyen, T.H. Nitsche’s Method for a Transport Problem in Two-phase Incompressible Flows. J Fourier Anal Appl 15, 663–683 (2009). https://doi.org/10.1007/s00041-009-9092-y
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DOI: https://doi.org/10.1007/s00041-009-9092-y