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Numerical Approximation of Large Contrast Problems with the Unfitted Nitsche Method

  • Erik Burman
  • Paolo Zunino
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 85)

Abstract

These notes are concerned with the numerical treatment of the coupling between second order elliptic problems that feature large contrast between their characteristic coefficients. In particular, we study the application of Nitsche’s method to set up a robust approximation of interface conditions in the framework of the finite element method. The notes are subdivided in three parts. Firstly, we review the weak enforcement of Dirichlet boundary conditions with particular attention to Nitsche’s method and we discuss the extension of such technique to the coupling of Poisson equations. Secondly, we review the application of Nitsche’s method to large contrast problems, discretised on computational meshes that capture the interface of discontinuity between coefficients. Finally, we extend the previous schemes to the case of unfitted meshes, which occurs when the computational mesh does not conform with the interface between subproblems.

Keywords

Bilinear Form Physical Domain Penalty Term Element Space Penalty Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Notes

Acknowledgements

The authors acknowledge the support of the project 5 per Mille Junior “”Computational models for heterogeneous media. Application to microscale analysis of tissue engineered constructs”, CUP D41J10000490001, Politecnico di Milano.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of SussexBrightonUK
  2. 2.MOX - Department of MathematicsPolitecnico di MilanoMilanoItaly

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