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A New Boundary Element Method for the Biharmonic Equation with Dirichlet Boundary Conditions

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Abstract

We consider a scalar boundary integral formulation for the biharmonic equation based on the Almansi representation. This formulation was derived by the first author in an earlier paper. Our aim here is to prove the ellipticity of the integral operator and hence establish convergence of and error bounds for Galerkin boundary element methods. The theory applies both in two and three dimensions, but only for star-shaped domains. Numerical results in two dimensions confirm our analysis.

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Authors and Affiliations

  1. Department of Mathematics, Ajou University, Suwon, 442-749, Korea

    Youngmok Jeon

  2. School of Mathematics, The University of New South Wales, Sydney, 2052, Australia

    William McLean

Authors
  1. Youngmok Jeon
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  2. William McLean
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Jeon, Y., McLean, W. A New Boundary Element Method for the Biharmonic Equation with Dirichlet Boundary Conditions. Advances in Computational Mathematics 19, 339–354 (2003). https://doi.org/10.1023/A:1024206232212

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