An iterative regularization method for a class of inverse boundary value problems of elliptic type

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 efficiency of this method.