摘要
讨论带有逐点控制约束条件的最优控制问题超收敛性.在有限元离散化中,控制变量用分片常函数近似,状态变量和伴随状态变量用分片线性函数近似,并重新构造控制变量u的插值uI.证明了状态方程为二维椭圆方程时,插值uI与控制u的有限元解uh的误差估计收敛阶为2.
In this paper,superconvergence analysis of an optimal control problem is investigated with pointwise control constraints.In the finite element approximation,control is approximated by piecewise constant functions and the state and the adjoint state are discretized by linear finite elements,then the interpolation uI of the control u is constructed.We prove that the convergence order is 2 between the interpolation uI and the finite element approximation uh for a 2-d elliptic equation.
出处
《河北工业大学学报》
CAS
北大核心
2011年第2期86-89,共4页
Journal of Hebei University of Technology
关键词
最优控制问题
椭圆方程
超收敛
误差估计
插值
收敛阶
optimal control problems
elliptic equations
superconvergence
error estimates
interpolation
convergence order
