一类椭圆最优控制问题的最大模估计

L^∞-Error Estimates for Quadratic Optimal Control Problem by Mixed Finite Element Methods

采用混合有限元方法研究一类椭圆最优控制问题的最大模估计.对状态变量和对偶状态变量,采用最低阶的R-T混合有限元空间来逼近;对控制变量采用分片常数函数来逼近.通过引入投影算子,找到了对偶状态变量和控制变量之间的关系,进而得到了关于状态变量及控制变量的最优阶误差估计.最后给出了相应的数值算例.

In this paper,we investigate the L∞-error estimates for the solutions of elliptic optimal control problem by mixed finite element methods.The state and co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise constant functions.By introducing the projection,we find the relation between the co-state variable and the control variable.We derive L∞-error estimates of optimal order both for the state variables and the control variable.At last,a numerical test is presented.