A robust data completion method for two dimensional Cauchy problems associated with the Laplace equation

Our aim is to propose an improved regularization method for data completion problems. This method is presented on the Cauchy problem for the Laplace equation in 2D situations. This method is an iterative one, uses a regularization with fading effect and penalization terms which take into account the fact that, under some regularity assumptions, the partial derivatives of a harmonic function is also harmonic. Many numerical simulations using the finite element method highlight the efficiency, accuracy, stability when data are noisy and the ability of the method to take into account and deblur noisy data.

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