A simplified Tikhonov regularization for solving a backward advection-dispersion problem

This paper studies a backward problem of an advection-dispersion equation, which is a severely ill-posed problem. The optimal and order optimal error bounds for the problem are given based on the a priori source conditions. Using a simplified Tikhonov regularization method, in different cases, by a priori and a posteriori parameter choice rules, the a priori and a posteriori order optimal error estimates, error estimates and convergence results for the problem are derived, respectively. Finally, numerical examples are conducted to show the effectiveness and stability of the proposed regularization method.