Tang Yuelong, Hua Yuchun
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.
J Inequal Appl. 2017;2017(1):62. doi: 10.1186/s13660-017-1334-y. Epub 2017 Mar 16.
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.
本文考虑了一种用于求解双线性抛物型最优控制问题的半离散有限元方法。首先，我们给出模型问题的有限元近似。其次，我们引入一些重要的中间变量及其误差估计。第三，我们推导近似格式的先验误差估计。最后，我们得到半离散有限元解与精确解投影之间的超收敛性。给出了一个数值例子来验证我们的理论结果。
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