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New boundary element formulas for the biharmonic equation

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Abstract

We propose two new boundary integral equation formulas for the biharmonic equation with the Dirichlet boundary data that arises from plate bending problems in ℝ2. Two boundary conditions, u and ∂u/∂n, usually yield a 2 × 2 non-symmetric matrix system of integral equations. Our new formulas yield scalar integral equations that can be handled more efficiently for theoretical and numerical purposes. In this paper we supply complete ellipticity and solvability analyses of our new formulas. Numerical experiments for simple Galerkin methods are also provided.

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Authors and Affiliations

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

    Youngmok Jeon

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  1. Youngmok Jeon
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Jeon, Y. New boundary element formulas for the biharmonic equation. Advances in Computational Mathematics 9, 97–115 (1998). https://doi.org/10.1023/A:1018985322648

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