Identifying an Unknown Source in the Poisson Equation with a Super Order Regularization Method

Abstract

This paper develops a new method to deal with the problem of identifying the unknown source in the Poisson equation. We obtain the regularization solution by the Tikhonov regularization method with a super-order penalty term. The order optimal error bounds can be obtained for various smooth conditions when we choose the regularization parameter by a discrepancy principle and the solution process of the new method is uniform. Numerical examples show that the proposed method is effective and stable.