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Analysis of the fully discrete fat boundary method

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Abstract

The Fat Boundary Method is a method of the Fictitious Domain class, which was proposed to solve elliptic problems in complex geometries with non-conforming meshes. It has been designed to recover optimal convergence at any order, despite of the non-conformity of the mesh, and without any change in the discrete Laplace operator on the simple shape domain. We propose here a detailed proof of this high-order convergence, and propose some numerical tests to illustrate the actual behaviour of the method.

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Authors and Affiliations

  1. Istituto di Matematica Applicata e Tecnologie Informatiche del C.N.R., v. Ferrata 1, 27100, Pavia, Italy

    Silvia Bertoluzza

  2. Laboratoire de Spectrométrie Physique, Université de Grenoble, BP 53, 38041, Grenoble Cedex 9, France

    Mourad Ismail

  3. Laboratoire de Mathématiques, Université Paris-Sud, 91405, Orsay cedex, France

    Bertrand Maury

Authors
  1. Silvia Bertoluzza
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  2. Mourad Ismail
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  3. Bertrand Maury
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Correspondence to Bertrand Maury.

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Bertoluzza, S., Ismail, M. & Maury, B. Analysis of the fully discrete fat boundary method. Numer. Math. 118, 49–77 (2011). https://doi.org/10.1007/s00211-010-0317-4

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  • DOI: https://doi.org/10.1007/s00211-010-0317-4

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