Author(s)

L. Marin, L. Elliott, D.B. Ingham & D. Lesnic

Abstract

Boundary element solution for the Cauchy problem in linear elasticity L. Marin, L. Elliott, D.B. Ingham & D. Lesnic Department of Applied Mathematics, University of Leeds, UK Abstract In this paper we investigate the solution of the Cauchy problem in lin- ear elasticity using the iterative algorithm proposed by Kozlov et al. [I] for obtaining approximate solutions to ill-posed boundary value problems. The technique is then numerically implemented using the boundary element method (BEM). The numerical results obtained confirm that the iterative BEM produces a convergent and stable numerical solution with respect to increasing the number of boundary elements and decreasing the amount of noise added into the input data. An efficient stopping regularizing criterion is given and in addition the accuracy of the iterative algorithm is improved by using a variable relaxation procedure. 1 Introduction Consider an isotropic linear elastic material which occupies an open bounded

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