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Finite element method for parallel slit mappings

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Abstract

We aim to establish a method of the finite element approximation by which we can construct the parallel slit mappings. It is characteristic of our method that we adopt ordinary triangular meshes and linear elements on a subregion of every fixed parametric disk, our triangulation embeds \({\overline{\Omega}}\) exactly even in the case of curvilinear boundary arcs, and our approximating functions of u express singular property exactly near inner and corner singularities. Our finite element approximations of the harmonic functions can be obtained by a combination of the method of the finite element approximations and the Schwarz’s alternative method. We apply our results to numerical calculations of the parallel mappings for the exterior domain of multielement airfoils etc.

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Authors and Affiliations

  1. Hiroshima University, Higashihiroshima, Japan

    Hisao Mizumoto

  2. Kawasaki University of Medical Welfare, Kurashiki, 701-0193, Japan

    Hisao Mizumoto

  3. Department of Health Informatics, Kawasaki University of Medical Welfare, 288 Matsushima, Kurashiki, 701-0193, Japan

    Heihachiro Hara

Authors
  1. Hisao Mizumoto
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  2. Heihachiro Hara
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Correspondence to Heihachiro Hara.

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Mizumoto, H., Hara, H. Finite element method for parallel slit mappings. Japan J. Indust. Appl. Math. 28, 263–299 (2011). https://doi.org/10.1007/s13160-011-0038-9

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  • DOI: https://doi.org/10.1007/s13160-011-0038-9

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