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A Cut Finite Element Method with Boundary Value Correction for the Incompressible Stokes Equations

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Numerical Mathematics and Advanced Applications ENUMATH 2017 (ENUMATH 2017)

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 126))

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Abstract

We design a cut finite element method for the incompressible Stokes equations on domains with curved boundary. The cut finite element method allows for the domain boundary to cut through the elements of the computational mesh in a very general fashion. To further facilitate the implementation we propose to use a piecewise affine discrete domain even if the physical domain has curved boundary. Dirichlet boundary conditions are imposed using Nitsche’s method on the discrete boundary and the effect of the curved physical boundary is accounted for using the boundary value correction technique introduced for cut finite element methods in Burman et al. (Math Comput 87(310):633–657, 2018).

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References

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Acknowledgements

This research was supported in part by EPSRC grant EP/P01576X/1, the Swedish Foundation for Strategic Research Grant No. AM13-0029, the Swedish Research Council Grants Nos. 2013-4708, 2017-03911, and the Swedish Research Programme Essence.

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Authors and Affiliations

  1. Department of Mathematics, University College London, London, UK

    Erik Burman

  2. Department of Mechanical Engineering, Jönköping University, Jönköping, Sweden

    Peter Hansbo

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

    Mats G. Larson

Authors
  1. Erik Burman
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  2. Peter Hansbo
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  3. Mats G. Larson
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Corresponding author

Correspondence to Erik Burman .

Editor information

Editors and Affiliations

  1. University of Bergen, Bergen, Norway

    Florin Adrian Radu

  2. University of Bergen, Bergen, Norway

    Kundan Kumar

  3. University of Bergen, Bergen, Norway

    Inga Berre

  4. University of Bergen, Bergen, Norway

    Jan Martin Nordbotten

  5. Hasselt University, Diepenbeek, Belgium

    Iuliu Sorin Pop

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Burman, E., Hansbo, P., Larson, M.G. (2019). A Cut Finite Element Method with Boundary Value Correction for the Incompressible Stokes Equations. In: Radu, F., Kumar, K., Berre, I., Nordbotten, J., Pop, I. (eds) Numerical Mathematics and Advanced Applications ENUMATH 2017. ENUMATH 2017. Lecture Notes in Computational Science and Engineering, vol 126. Springer, Cham. https://doi.org/10.1007/978-3-319-96415-7_15

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