Advances in Computational Mathematics

, Volume 19, Issue 4, pp 339–354 | Cite as

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

  • Youngmok Jeon
  • William McLean


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.

biharmonic equations Almansi representation layer potential boundary integral equation 


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Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Youngmok Jeon
    • 1
  • William McLean
    • 2
  1. 1.Department of MathematicsAjou UniversitySuwonKorea
  2. 2.School of MathematicsThe University of New South WalesSydneyAustralia

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