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

  • Erik Burman
  • Alexandre ErnEmail author
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 126)


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 H1-norm.



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.


  1. 1.
    J.W. Barrett, C.M. Elliott, Fitted and unfitted finite-element methods for elliptic equations with smooth interfaces. IMA J. Numer. Anal. 7(3), 283–300 (1987)MathSciNetCrossRefGoogle Scholar
  2. 2.
    L. Botti, D.A. Di Pietro, Assessment of hybrid high-order methods on curved meshes and comparison with discontinuous Galerkin methods (2017). HAL e-print hal-01581883Google Scholar
  3. 3.
    E. Burman, Ghost penalty. C. R. Math. Acad. Sci. Paris 348(21–22), 1217–1220 (2010)MathSciNetCrossRefGoogle Scholar
  4. 4.
    E. Burman, A. Ern, An unfitted hybrid high-order method for elliptic interface problems (2017). ArXiv e-print 1710.10132Google Scholar
  5. 5.
    D.A. Di Pietro, A. Ern, A Hybrid High-Order locking-free method for linear elasticity on general meshes. Comput. Meth. Appl. Mech. Eng. 283(1), 1–21 (2015)MathSciNetCrossRefGoogle Scholar
  6. 6.
    D.A. Di Pietro, A. Ern, S. Lemaire, An arbitrary-order and compact-stencil discretization of diffusion on general meshes based on local reconstruction operators. Comput. Meth. Appl. Math. 14(4), 461–472 (2014)MathSciNetCrossRefGoogle Scholar
  7. 7.
    V. Girault, R. Glowinski, Error analysis of a fictitious domain method applied to a Dirichlet problem. Jpn. J. Indust. Appl. Math. 12(3), 487–514 (1995)MathSciNetCrossRefGoogle Scholar
  8. 8.
    A. Hansbo, P. Hansbo, An unfitted finite element method, based on Nitsche’s method, for elliptic interface problems. Comput. Methods Appl. Mech. Eng. 191(47–48), 5537–5552 (2002)MathSciNetCrossRefGoogle Scholar
  9. 9.
    A. Johansson, M.G. Larson, A high order discontinuous Galerkin Nitsche method for elliptic problems with fictitious boundary. Numer. Math. 123(4), 607–628 (2013)MathSciNetCrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.Department of MathematicsUniversity College LondonLondonUK
  2. 2.Université Paris-EstCERMICS (ENPC)Marne-la-Vallée CedexFrance
  3. 3.INRIA ParisParisFrance

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