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Deriving Robust Unfitted Finite Element Methods from Augmented Lagrangian Formulations

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Geometrically Unfitted Finite Element Methods and Applications

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 121))

Abstract

In this paper we will discuss different coupling methods suitable for use in the framework of the recently introduced CutFEM paradigm, cf. Burman et al. (Int. J. Numer. Methods Eng. 104(7):472–501, 2015). In particular we will consider mortaring using Lagrange multipliers on the one hand and Nitsche’s method on the other. For simplicity we will first discuss these methods in the setting of uncut meshes, and end with some comments on the extension to CutFEM. We will, for comparison, discuss some different types of problems such as high contrast problems and problems with stiff coupling or adhesive contact. We will review some of the existing methods for these problems and propose some alternative methods resulting from crossovers from the Lagrange multiplier framework to Nitsche’s method and vice versa.

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Acknowledgements

The contribution of the first author was supported in part by the EPSRC grants EP/J002313/2 and EP/P01576X/1, the contribution of the second author was supported in part by the Swedish Foundation for Strategic Research Grant No. AM13-0029 and the Swedish Research Council Grant No. 2011-4992.

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Authors and Affiliations

  1. Department of Mathematics, University College London, London, WC1E 6BT, UK

    Erik Burman

  2. Department of Mechanical Engineering, Jönköping University, SE-55111, Jönköping, Sweden

    Peter Hansbo

Authors
  1. Erik Burman
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  2. Peter Hansbo
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Correspondence to Erik Burman .

Editor information

Editors and Affiliations

  1. Faculté des Sciences, de la Technologie et de la Communication, Université du Luxembourg, Luxembourg

    Stéphane P. A. Bordas

  2. Department of Mathematics, University College London, United Kingdom

    Erik Burman

  3. Department of Mathematics and Mathematical Statistics, Umeå University, Sweden

    Mats G. Larson

  4. Department of Mathematics, University of Houston, USA

    Maxim A. Olshanskii

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Burman, E., Hansbo, P. (2017). Deriving Robust Unfitted Finite Element Methods from Augmented Lagrangian Formulations. In: Bordas, S., Burman, E., Larson, M., Olshanskii, M. (eds) Geometrically Unfitted Finite Element Methods and Applications. Lecture Notes in Computational Science and Engineering, vol 121. Springer, Cham. https://doi.org/10.1007/978-3-319-71431-8_1

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