Penalty-Free Nitsche Method for Interface Problems

  • Thomas Boiveau
  • Erik Burman
  • Susanne Claus
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 121)


Nitsche’s method is a penalty-based method to weakly enforce boundary conditions in the finite element method. In this paper, we present a penalty free version of Nitsche’s method to impose interface coupling in the framework of unfitted domain decomposition. Unfitted domain decomposition is understood in the sense that the interface between the domains can cross elements of the mesh arbitrarily. The pure diffusion problem with discontinuous material parameters is considered for the theoretical study, we show the convergence of the L2 and H1-error for high contrast in the diffusivities. Then, we give the corresponding numerical results for the pure diffusion problem, additionally we consider the Stokes problem. We compare the performance of the penalty free method with the more classical symmetric and nonsymmetric Nitsche’s methods for different cases, including for the error generated in the interface fluxes.



This work received funding from EPSRC (award number EP/J002313/2) which is gratefully acknowledged. The Author, S. Claus, gratefully acknowledges the financial support provided by the Welsh Government and Higher Education Funding Council for Wales through the Sêr Cymru National Research Network in Advanced Engineering and Materials.


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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Université Paris-EstCERMICS (ENPC)Marne-la-Vallée 2France
  2. 2.Inria ParisParisFrance
  3. 3.Department of MathematicsUniversity College LondonLondonUK
  4. 4.Cardiff School of EngineeringCardiff UniversityCardiffUK

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