L^∞-error estimates of rectangular mixed finite element methods for bilinear optimal control problem

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• 作者：Zuliang Lu^a ; ^b ; ^{zulianglux@126.com} ; Shuhua Zhang ; ^b ; ^{shuhua55@126.com} ; ^{szhang@tjufe.edu.cn}
• 关键词：Bilinear optimal control problem ; Raviart&ndash ; Thomas mixed finite element methods ; Rectangular partition ; L&infin ; -error estimates
• 刊名：Applied Mathematics and Computation
• 出版年：2017
• 出版时间：1 May 2017
• 年：2017
• 卷：300
• 期：Complete
• 页码：79-94
• 全文大小：539 K
• 卷排序：300

文摘

In this paper, we investigate L∞-error estimates of the bilinear elliptic optimal control problem by rectangular Raviart–Thomas mixed finite element methods. The control variable enters the state equation as a coefficient. The state and the co-state variables are approximated by the Raviart–Thomas mixed finite elements of order k=1,k=1, and the control variable is approximated by piecewise linear functions. The L∞-error estimates are obtained for the control variable and coupled state variable, and the convergence rates of orders O(h2) and O(h32|lnh|12) are also gained for the control and state variables and the flux of the state and co-state variables, respectively. In addition, the performance of the error estimates is assessed by two numerical examples.