A Directly Numerical Algorithm for a Backward Time-Fractional Diffusion Equation Based on the Finite Element Method

Abstract EN

We study a backward problem for a time-fractional diffusion equation, which is formulated into a regularized optimization problem.

After solving a sequence of well-posed direct problems by the finite element method, a directly numerical algorithm is proposed for solving the regularized optimization problem.

In order to obtain a reasonable regularization solution, we utilize the discrepancy principle with decreasing geometric sequence to choose regularization parameters.

One- and two-dimensional examples are given to verify the efficiency and stability of the proposed method.