Numerical solution of a nonlinear parabolic inverse problem using optimal control and finite element methods

Abstract

This paper deals with numerical approximations of an identification inverse problem governed by a highly nonlinear parabolic equation. In order to solve our problem, an optimal control formulation is proposed. The associated optimization problem is solved using a gradient-type method. The nonlinear state problem is discretized by the finite element scheme and solved by Newton's method. Finally, to demonstrate the efficiency of the proposed approach, numerical experiments are presented.