Finite element approximations of impulsive optimal control problems for heat equations

摘要

In this paper we study the priori error analysis for semidiscrete Galerkin finite element approximation of the impulsive optimal control problem governed by linear heat equation with control constraint. We first derive Pontryagin's maximum principle and construct the semidiscrete finite element approximation scheme for our impulsive optimal control problem. Then, the error estimates for optimal control u, the related state y and the adjoint state phi will be obtained. Finally, an efficient algorithm for our numerical experiment is designed, which verifies the theoretical results obtained in this paper. (C) 2019 Elsevier Inc. All rights reserved.