A priori error estimates of finite volume element method for hyperbolic optimal control problems

作者：Luo XianBing; Chen YanPing^*; Huang YunQing

来源：Science China Mathematics, 2013, 56(5): 901-914.

DOI：10.1007/s11425-013-4573-5

• second order hyperbolic equation
• optimal control problems
• finite volume element method
• distributed control
• variational discretization

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 (a)(J;L (2))- and L (a)(J;H (1))-norm. Numerical experiments are presented to test these theoretical results.

• 单位
  华南师范大学; 湘潭大学