An alternating iterative algorithm for the Cauchy problem in anisotropic elasticity

The alternating iterative algorithm proposed by Kozlov et al. [An iterative method for solving the Cauchy problem for elliptic equations. USSR Comput Math Math Phys 1991;31:45–52] for obtaining approximate solutions to the Cauchy problem in two-dimensional anisotropic elasticity is analysed and numerically implemented using the boundary element method (BEM). The ill-posedness of this inverse boundary value problem is overcome by employing an efficient regularising stopping. The numerical results 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.