Title: Explicit error estimates in a method of moments for recovering boundary data

Authors: Boujemâa Achchab; Abdeljalil Sakat; Ali Souissi

Addresses: Laboratory of Analysis and Modeling Systems for Decision Support, Department of Mathematics and Computer Engineering, ENSA, Hassan 1 University, B.P. 218 Berrechid 26100, Morocco ' Laboratory of Analysis and Modeling Systems for Decision Support, Department of Mathematics and Computer Engineering, ENSA, Hassan 1 University, B.P. 218 Berrechid 26100, Morocco ' Numerical Analysis Group, Department of Mathematics, Faculty of Sciences, Mohammed V University, Post-Office Box No. 1014, 4 Ibn Battouta Avenue, PC 10090 Rabat, Morocco

Abstract: We consider a data completion method for the Cauchy problem of Laplace equation, that is known as a highly ill-posed problem. For an approximate solution given by any one of algorithms of the data completion methods, we give the moment of the error between the true solution and the approximate one, which allows us to find an a posteriori explicit error estimation. This error indicator is used to improve the approximate solution, to give a knowledge of stability and can be used as a stopping criterion. Eventually, numerical experiments are provided.

Keywords: Cauchy problem; Laplace equation; data completion problem; explicit a posteriori error estimate; moment problem; stopping criterion.

DOI: 10.1504/IJMMNO.2021.116680

International Journal of Mathematical Modelling and Numerical Optimisation, 2021 Vol.11 No.3, pp.232 - 251

Received: 31 Jan 2020
Accepted: 23 Jul 2020
Published online: 29 Jul 2021 *

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