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European Conference on Numerical Mathematics and Advanced Applications

ENUMATH 2017: Numerical Mathematics and Advanced Applications ENUMATH 2017 pp 173–181Cite as

A Cut Cell Hybrid High-Order Method for Elliptic Problems with Curved Boundaries

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

Abstract

We design a Hybrid High-Order method for elliptic problems on curved domains. The method uses a cut cell technique for the representation of the curved boundary and imposes Dirichlet boundary conditions using Nitsche’s method. The physical boundary can cut through the cells in a very general fashion and the method leads to optimal error estimates in the H 1-norm.

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Acknowledgements

The first author was partly supported by EPSRC Grant EP/P01576X/1. This work was initiated when the authors were visiting the Institut Henri Poincaré during the Fall 2016 Thematic Trimester “Numerical Methods for Partial Differential Equations”. The support of IHP is gratefully acknowledged.

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Authors and Affiliations

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

    Erik Burman

  2. Université Paris-Est, CERMICS (ENPC), Marne-la-Vallée Cedex, France

    Alexandre Ern

  3. INRIA Paris, Paris, France

    Alexandre Ern

Authors
  1. Erik Burman
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  2. Alexandre Ern
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Corresponding author

Correspondence to Alexandre Ern .

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., Ern, A. (2019). A Cut Cell Hybrid High-Order Method for Elliptic Problems with Curved Boundaries. 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_14

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