On the approximation of a Cauchy problem in a non-homogeneous medium

F. Aboud (1) , Abdeljalil Nachaoui (2) , M. Nachaoui (3)

1 Mathematics Department, College of Sciences, University of Diyala
2 LMJL - Laboratoire de Mathématiques Jean Leray
3 Laboratoire de Mathématiques et Applications, FST, Beni-Mellal, Maroc

This paper deals with an inverse Cauchy problem governed by an elliptical equation defined in non-homogeneous domain. We propose two approaches based on alternating algorithm [Nachaoui A., Nachaoui A., Chakib A. and Hilal M.A., Some novel numerical techniques for an inverse Cauchy problem,J. Comput. Appl. Math., 381 (2021), 113030] combined with a domain decomposition method. We use the finite elements method to approximate the associate direct problems. Finally, we show the numerical convergence of both proposed algorithms and we discuss there efficiency trough some numerical experiments.

Mots clés: Inverse Cauchy problem; Domain decomposition; Iterative algorithms; Finite elements FE

Domaines: Mathématiques [math]; Analyse numérique [math.NA]

F. Aboud, Abdeljalil Nachaoui, M. Nachaoui. On the approximation of a Cauchy problem in a non-homogeneous medium. Journal of Physics: Conference Series, 2021, 1743, pp.012003. ⟨10.1088/1742-6596/1743/1/012003⟩. ⟨hal-03118140⟩