Journal of Mathematical Physics, Analysis, Geometry 2020, vol. 16, No 1, pp. 66-85   https://doi.org/10.15407/mag16.01.066     ( to contents , go back )

### An Iterative Regularization Method for a Class of Inverse Boundary Value Problems of Elliptic Type

Fairouz Zouyed

Applied Math Lab, University Badji Mokhtar-Annaba, P.O.Box. 12, Annaba 23000, Algeria
E-mail: fzouyed@gmail.com

Souheyla Debbouche

Department of Mathematics, University Larbi Ben M'hidi, Oum El Bouaghi, Algeria
E-mail: Souheyla.prof@gmail.com

Received October 15, 2018, revised November 16, 2018.

Abstract

This paper deals with the problem of determining an unknown source and an unknown boundary condition $u (0)$ in a boundary value problem of elliptic type from extra measurements at internal points. The problem is ill-posed in the sense that the solution (if it exists) does not depend continuously on the data. For solving the considered problem an iterative method is proposed. Using this method a regularized solution is constructed and an a priori error estimate between the exact solution and its regularization approximation is obtained. Moreover, the numerical results are presented to illustrate the accuracy and effciency of this method.

Mathematics Subject Classification 2000: 35J25, 47A52, 65M32.
Key words: inverse problems, ill-posed problems, elliptic problems, iterative regularization method.