On the identification of discontinuous matrix diffusion in elliptic equation

Abstract

The aim of this paper is to study the identification a discontinuous matrix diffusion parameter in the elliptic partial differential equation considered with mixed non-homogenous boundary conditions on a boundary of bounded open subset domain in two dimensional space. This parameter is taken as a matrix valued on bounded variation space . The observation can be partially or globally given in the domain into consideration. We reformulate the associated inverse problem to an optimization one, we prove the existence of solution and we study the discrete case by using finite element method and we expose a result of the convergence of the solution of the discrete problem to continuous one. We describe an optimization algorithm and the numerical results are discussed in the end.