一类最优控制问题混合有限元解的后验误差估计

journal6 ›› 2010, Vol. 31 ›› Issue (2): 29-32.

一类最优控制问题混合有限元解的后验误差估计

(1.湖南信息科学职业学院,湖南长沙 410175;2.河南农业大学华豫学院,河南商丘 476100;3.湖南工业大学科技学院,湖南株洲 412008)

出版日期:2010-03-25 发布日期:2012-04-18
作者简介:傅敏（1981-），女，湖南洞口人，湖南信息科学职业学院教师，主要从事有限元研究.

Posteriori Error Estimates for Mixed Finite Element Solutions of Optimal Control Problems

(1.Hunan Vocational College of Information Science,Changsha 410175,China;2.Huayu College of Henan Agricultural University,Shangqiu 476000,He’nan China;3.Science Technology College of Hunan Technology University,Zhuzhou 412008,Hunan China)

Online:2010-03-25 Published:2012-04-18

摘要/Abstract

摘要：对一类受非线性椭圆方程约束的二次最优控制问题的混合有限元方法进行了后验误差分析.利用k阶R-T混合元空间和分片常数函数分别对状态变量和控制变量进行估计,得到合适的后验误差指示子.在数值实验中将所得的后验误差指示子作为网格加密的指示子,得到较为精确的数值解.

关键词： 非线性最优控制, 混合有限元逼近, 后验误差估计

Abstract: An a posteriori error analysis is obtained for mixed finite element approximation of quadratic convex optimal control problem governed by nonlinear elliptic equation.The state and the co-state are approximated by the k-th R-T mixed finite element spaces and the control is approximated by piecewise constant functions.The results are based on the approximation for both the state variables and the control variable.In numerical experiments,the posteriori error estimators are used as the mesh refinement indicator.Then it is clear that the adaptive finite element method is more efficient.

Key words: nonlinear optimal control, mixed finite element approximation, posteriori error estimates

傅敏, 刁林, 罗超良. 一类最优控制问题混合有限元解的后验误差估计[J]. journal6, 2010, 31(2): 29-32.

FU Min, DIAO Lin, LUO Chao-Liang. Posteriori Error Estimates for Mixed Finite Element Solutions of Optimal Control Problems[J]. journal6, 2010, 31(2): 29-32.