Numerical Study of Inverse Source Problem for Internal Degenerate Parabolic Equation

Abstract

This paper is devoted to numerical analysis of an inverse source problem in a degenerate parabolic equation. The aims of this work are to show the well-posedness of the discrete inverse problem and its convergence to the continuous one. For this, we reformulate first the encountered inverse problem to a regularized optimal control one. Then, we approximate our optimal control problem by finite element method and we show the existence of the discrete solution and its convergence to the continuous one. Finally, in order to confirm the efficiency of the proposed scheme, some numerical results are obtained using the augmented Lagrangian method.