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A priori error estimates of finite volume element method for hyperbolic optimal control problems 被引量:5

A priori error estimates of finite volume element method for hyperbolic optimal control problems
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摘要 In this paper,optimize-then-discretize,variational discretization and the finite volume method are applied to solve the distributed optimal control problems governed by a second order hyperbolic equation.A semi-discrete optimal system is obtained.We prove the existence and uniqueness of the solution to the semidiscrete optimal system and obtain the optimal order error estimates in L ∞(J;L 2)-and L ∞(J;H 1)-norm.Numerical experiments are presented to test these theoretical results. In this paper, optimize-then-discretize, variational discretization and the finite volume method are applied to solve the distributed optimal control problems governed by a second order hyperbolic equation. A semi-discrete optimal system is obtained. We prove the existence and uniqueness of the solution to the semi- discrete optimal system and obtain the optimal order error estimates in L∞(J;L2)- and L∞(J;H1)-norm. Numerical experiments are presented to test these theoretical results.
出处 《Science China Mathematics》 SCIE 2013年第5期901-914,共14页 中国科学:数学(英文版)
基金 supported by National Natural Science Foundation of China(Grant Nos.11261011,11271145 and 11031006) Foundation of Guizhou Science and Technology Department(Grant No.[2011]2098) Foundation for Talent Introduction of Guangdong Provincial University Specialized Research Fund for the Doctoral Program of Higher Education(Grant No. 20114407110009) the Project of Department of Education of Guangdong Province(Grant No. 2012KJCX0036)
关键词 second order hyperbolic equation optimal control problems finite volume element method dis- tributed control variational discretization 二阶双曲型方程 最优控制问题 先验误差估计 有限体积法 优化系统 数值实验 离散化 半离散
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