title: Superconvergence of semidiscrete finite element methods for bilinear parabolic optimal control problems.
abstract: In this paper, a semidiscrete finite element method for solving bilinear parabolic optimal control problems is considered. Firstly, we present a finite element approximation of the model problem. Secondly, we bring in some important intermediate variables and their error estimates. Thirdly, we derive a priori error estimates of the approximation scheme. Finally, we obtain the superconvergence between the semidiscrete finite element solutions and projections of the exact solutions. A numerical example is presented to verify our theoretical results.
authors.affiliation: Institute of Computational Mathematics, College of Science, Hunan University of Science and Engineering, Yongzhou, Hunan 425100 China.|Office of Continuing Education, Peking University, Beijing, 100871 China.
authors.forename: Yuelong
authors.initials: Y
authors.lastname: Tang
authors.affiliation: Institute of Computational Mathematics, College of Science, Hunan University of Science and Engineering, Yongzhou, Hunan 425100 China.
authors.forename: Yuchun
authors.initials: Y
authors.lastname: Hua
keywords: bilinear parabolic optimal control problems; finite element method; superconvergence