Convergence study and regularizing property of a modified Robin–Robin method for the Cauchy problem in linear elasticity. (1st July 2022)

• Record Type: Journal Article
• Authors: Ellabib, Abdellatif; Nachaoui, Abdeljalil; Ousaadane, Abdessamad
• Is Part Of: Inverse problems. Volume 38:Number 7(2022)
• Publication Date: 2022-07-01
• Subjects: Cauchy problem -- convergence -- elasticity equation -- finite element method -- numerical stability -- regularizing property -- Robin condition; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/ac70f3
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: In this paper, we are interested in solving a Cauchy inverse problem in linear elasticity. For this, we propose a new method based on Robin conditions on the inaccessible boundary, then we study the convergence and regularizing property of the proposed algorithm. We use the finite element method for the discretization of our problem. Further, we treat the spectrum analysis of the discrete problem in order to study the convergence behavior of the proposed method in the discrete case. Finally, we present numerical results which show the efficiency and stability of the proposed approach in the presence of perturbed data. The robustness of the proposed algorithm is also performed for the anisotropic and heterogeneous cases.