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Superconvergence of semidiscrete finite element methods for bilinear parabolic optimal control problems
Yuelong Tang1,2, Yuchun Hua1
1Institute of Computational Mathematics, College of Science, Hunan University of Science and Engineering, Yongzhou, Hunan 425100 China.
Journal of Inequalities and Applications
|April 4, 2017
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.