Numerical approximation for a time optimal control problems governed by semi-linear heat equations

被引：0
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作者：
Guojie Zheng
Jingben Yin
机构：
[1] Henan Normal University,College of Mathematics and Information Science
[2] University of the Witwatersrand,School of Computational and Applied Mathematics
[3] Henan Institute of Science and Technology,Department of Mathematics
来源：
Advances in Difference Equations | / 2014卷
关键词：
heat equation; time optimal control; finite element methods; numerical approximation;
D O I：
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学科分类号：
摘要：
In this paper, we study the optimal time for a time optimal control problem (P), governed by an internally controlled semi-linear heat equation. By projecting the original problem via the finite element method, we obtain another time optimal control problem (Ph) governed by a semi-linear system of ordinary differential equations. Here, h is the mesh sizes of the finite element spaces. The purpose of this study is to approach the optimal time for the problem (P) through the optimal time for the problem (Ph). We obtain error estimates between the optimal times in terms of h.
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