Inverse source identification by the modified regularization method on Poisson equation (Q411138)

Summary: This paper deals with an inverse problem for identifying an unknown source which depends only on one variable in two-dimensional Poisson equation, with the aid of an extra measurement at an internal point. Since this problem is ill-posed, we obtain the regularization solution by the modified regularization method. Furthermore, we obtain the Hölder-type error estimate between the regularization solution and the exact solution. The numerical results show that the proposed method is stable and the unknown source is recovered very well.