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Analysis of an efficient finite element method for embedded interface problems. (English) Zbl 1190.65172
Summary: A stabilized finite element method based on the Nitsche technique for enforcing constraints leads to an efficient computational procedure for embedded interface problems, in which the finite element mesh need not be aligned with the interface geometry. We consider cases in which the jump of a field across the interface is given, as well as cases in which the primary field on the interface is given. Optimal rates of convergence hold. Representative numerical examples demonstrate the effectiveness of the proposed methodology.

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
76F10 Shear flows and turbulence
76M10 Finite element methods applied to problems in fluid mechanics
Software:
XFEM
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References:
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