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a b s t r a c tThis work deals with the Cauchy problem in two-dimensional linear elasticity. The equations of the problem are discretized through a standard FEM approach and the resulting ill-conditioned discrete problem is solved within the frame of the Tikhonov approach, the choice of the required regularization parameter is accomplished through the Generalized Cross Validation criterion. On this basis a numerical experimentation has been performed and the calculated solutions have been used to highlight the sensitivity to the amount of known data, the noise always present in the data, the regularity of boundary conditions and the choice of the regularization parameter. The aim of the numerical study is to implicitly device some guidelines to be used in the solution of this kind of problems.

We test the performance of a three-dimensional finite element, named HC(3), which generalizes the high-continuity (HC) finite element proposed by Aristodemo in 1985 for two-dimensional elastic problems. The HC(3) finite element is based on a quadratic B-spline interpolation of the displacement field in three-dimensional linear elasticity. The main feature of this interpolation technique, which can be considered as a particular case of the Bezier interpolation, consists in its capability in reproducing displacement fields of C(1) smoothness with a computational cost equivalent to a linear interpolation, i.e. with a single knot for each element

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