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.
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)
