An energy-like error functional is introduced in the context of the ill-posed problem of boundary data recovering, which is well known as a Cauchy problem. Links with existing methods for data completion are detailed. Here the problem is converted into an optimization problem; the computation of the gradients of the energy-like functional is given for both the continuous and the discrete problems. Numerical experiments highlight the efficiency of the proposed method as well as its robustness in the model context of Laplace's equation, but also for anisotropic conductivity problems.

International audienceThe safety of turbomachines requires controlling the risks caused by contacts occurring between fixed and rotating parts. Undesirable phenomena induced by bladed wheel/casing interactions are caused by the forced excitation of the natural modes of a blade leading to its damage or by potentially dangerous couplings between the modes of the casing and those of the wheel. Rotor-stator contacts may also lead to various types of dangerous behavior, including the well known configurations of dry whirl and dry whip. The paper proposes a large-scale literature review and examines existing numerical models and experimental setups used for highlighting the phenomenology involved in different rotor to stator contacts configurations. It confirms the great complexity of the problems which, by nature, are considerably nonlinear and involve multiphysics and multiscale coupled behaviors

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