Boundary element method for the Cauchy problem in linear elasticity

In this paper, the iterative algorithm proposed by Kozlov et al. [Comput Ma ths Math Phys 32 (1991) 45] for obtaining approximate solutions to ill-pose d boundary value problems in linear elasticity is analysed. The technique i s then numerically implemented using the boundary element method (BEM). The numerical results obtained confirm that the iterative BEM produces a conve rgent and stable numerical solution with respect to increasing the number o f boundary elements and decreasing the amount of noise added into the input data. An efficient stopping regularizing criterion is given and in additio n, the accuracy of the iterative algorithm is improved by using a variable relaxation procedure. Analytical formulae for the integration constants res ulting from the direct application of the BEM for an isotropic linear elast ic medium are also presented. (C) 2001 Elsevier Science Ltd. All rights res erved.