线性双曲最优控制问题的P^(2)_(0)-P_(1)混合有限元方法的先验误差估计

A Priori Error Estimation of P^(2)_(0)-P_(1)Mixed Finite Element Methods for Linear Hyperbolic Optimal Control Problems

针对线性双曲最优控制问题,通过非标准的P^(2)_(0)-P_(1)混合有限元方法,利用椭圆投影、标准L^(2)投影、标准L^(2)-正交投影算子等理论,其中状态和对偶状态采用P^(2)_(0)-P_(1)混合有限元逼近,控制变量采用分片常数逼近,给出问题模型中所有变量的先验误差估计.

For the linear hyperbolic optimal control problem,by means of non-standard P^(2)_(0)-P_(1)mixed finite element method,using the theory of elliptic projection and the standard L^(2)-orthogonal projection,a priori error estimates of all variables for the model problem are given.The state and the co-state are approximated by P^(2)_(0)-P_(1)mixed finite element,and the control variable is approximated by the piecewise constant functions.