Convergence analysis for finite element approximation to an inverse Cauchy problem

In this paper, we propose an approximate optimal control formulation of the Cauchy problem, for an elliptic equation, equivalent to the original one under some regularity assumptions on the data. We prove the existence of a solution and show the convergence of a subsequence of approximate solutions, obtained via finite element approximation, to a solution of the continuous problem. Finally, we give some numerical results showing the efficiency of our approach and confirming the convergence result.