Open AccessA robust data completion method for two dimensional Cauchy problems associated with the Laplace equation
Author(s) -
Franck Delvare,
Alain Cimetière
Publication year - 2011
Publication title -
european journal of computational mechanics
Language(s) - English
Resource type - Journals
eISSN - 2642-2085
pISSN - 2642-2050
DOI - 10.13052/ejcm.20.309-340
Subject(s) - regularization (linguistics) , laplace transform , cauchy distribution , mathematics , laplace's equation , harmonic function , cauchy problem , stability (learning theory) , noisy data , finite element method , initial value problem , mathematical optimization , algorithm , mathematical analysis , computer science , partial differential equation , artificial intelligence , machine learning , physics , thermodynamics
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.