Two regularization methods for inverse source problem on the Poisson equation

This paper is devoted to discuss an inverse problem of determining an unknown source on the Poisson equation. This is a mildly ill-posed problem. Two regularization methods, one based on the mollification of the data and the other based on the modification of the kernel' of the solution, are proposed to solve this problem. The convergence estimates between the exact solution and the regularization solution are presented using a priori regularization parameter choice rule. Numerical results are presented to illustrate the accuracy and efficiency of the proposed methods.