Author(s)

A. Zeb, L. Elliott, D.B. Ingham and D. Lesnic

Abstract

The boundary element method is applied to discretise numerically the Cauchy problem for the biharmonic equation which arises in slow viscous flow problems. The resulting ill-conditioned system of linear equations is solved using the least squares and the minimal energy methods. The numerical solution is compared with a known analytical solution and it is shown that the least squares method is unstable but the minimal energy method is stable. 1 Introduction The Cauchy problem for the Laplace equation is a classical example of an ill-posed problem, which arises in many physical situations, and such problems have been extensively studied over the last 50 years, see for example Lavrentiev [7], Payne [10] & [11], Han [3], Lesnic et al. [8] and Zeb et al [12]. However, when it comes to the biharmonic equation, the

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