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Numerical Approximation of Large Contrast Problems with the Unfitted Nitsche Method

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Frontiers in Numerical Analysis - Durham 2010

Part of the book series: Lecture Notes in Computational Science and Engineering ((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.

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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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Authors and Affiliations

  1. Department of Mathematics, University of Sussex, Falmer, Brighton, BN1 9RF, UK

    Erik Burman

  2. MOX - Department of Mathematics, Politecnico di Milano, P.zza Leonardo da Vinci 32, 20133, Milano, Italy

    Paolo Zunino

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  1. Erik Burman
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Correspondence to Paolo Zunino .

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  1. , Department of Mathematical Sciences, Durham University, South Road, Durham, DH1 3LE, United Kingdom

    James Blowey

  2. , Department of Mathematical Sciences, Durham University, South Road, Durham, DH1 3LE, United Kingdom

    Max Jensen

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Burman, E., Zunino, P. (2011). Numerical Approximation of Large Contrast Problems with the Unfitted Nitsche Method. In: Blowey, J., Jensen, M. (eds) Frontiers in Numerical Analysis - Durham 2010. Lecture Notes in Computational Science and Engineering, vol 85. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23914-4_4

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