Deriving Robust Unfitted Finite Element Methods from Augmented Lagrangian Formulations

Conference paper
First Online:
Part of the Lecture Notes in Computational Science and Engineering book series (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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Notes

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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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of MathematicsUniversity College LondonLondonUK
  2. 2.Department of Mechanical EngineeringJönköping UniversityJönköpingSweden

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