L 1 -ERROR ESTIMATES FOR GENERAL OPTIMAL CONTROL PROBLEM BY MIXED FINITE ELEMENT METHODS
L 1 -ERROR ESTIMATES FOR GENERAL OPTIMAL CONTROL PROBLEM BY MIXED FINITE ELEMENT METHODS
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发表时间：
2008
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通讯作者：
X. Xing;Yanping Chen
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作者：
X. Xing;Yanping Chen
本文研究了椭圆型最优控制问题的混合有限元方法解的L∞误差估计.状态和余状态用最低阶Raviart-Thomas混合有限元空间逼近，控制用分段常数函数逼近.通过引入投影，得到了协状态变量与控制变量之间的关系，得到了状态变量和控制变量的最优阶的L∞-误差估计，最后，给出了数值试验。
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.