An Embedded Compact Scheme for Biharmonic Problems in Irregular Domains

  • Matania Ben-Artzi
  • Jean-Pierre CroisilleEmail author
  • Dalia Fishelov
Part of the Studies in Computational Intelligence book series (SCI, volume 728)


In Ben-Artzi et al. (SIAM J Numer Anal 47:3087–3108 (2009), [1]) a Cartesian embedded finite difference scheme for biharmonic problems has been introduced. The design of the scheme relies on a 19-dimensional polynomial space. In this paper, we show how to simplify the implementation by introducing a directional decomposition of this space. The boundary is handled via a level-set approach. Numerical results for non convex domains demonstrate the fourth order accuracy of the scheme.


  1. 1.
    Ben-Artzi, M., Chorev, I., Croisille, J.-P., Fishelov, D.: A compact difference scheme for the biharmonic equation in planar irregular domains. SIAM J. Numer. Anal. 47, 3087–3108 (2009)Google Scholar
  2. 2.
    Ben-Artzi, M., Croisille, J.-P., Fishelov, D.: A fast direct solver for the biharmonic problem in a rectangular grid. SIAM J. Sci. Comput. 31, 303–333 (2008)Google Scholar
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    Ben-Artzi M., Croisille J.-P., Fishelov, D.: Navier-Stokes Equations in Planar Domains. Imperial College Press (2013)Google Scholar
  4. 4.
    Chen, G., Li, Z., Lin, P.: A fast finite difference method for biharmonic equations on irregular domains and its application to an incompressible Stokes flow. Adv. Comput. Math. 2008, 113–133 (2008)Google Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Matania Ben-Artzi
    • 1
  • Jean-Pierre Croisille
    • 2
    Email author
  • Dalia Fishelov
    • 3
  1. 1.Institute of Mathematics, The Hebrew UniversityJerusalemIsrael
  2. 2.Department of MathematicsIECL, UMR CNRS 7502, Université de LorraineMetzFrance
  3. 3.Afeka Tel Aviv Academic College of EngineeringTel-AvivIsrael

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