• 论文 •

### 椭圆最优控制问题分裂正定混合有限元方法的超收敛性分析

1. 湖南科技学院, 永州 425199
• 收稿日期:2020-06-30 出版日期:2021-11-14 发布日期:2021-11-12
• 基金资助:
国家自然科学基金项目（11401201），湖南省自然科学基金项目（2020JJ4323），湖南省教育厅科学研究项目（20A211，20C0854），湖南科技学院科学研究项目（18XKY063，20XKY059），湖南科技学院应用特色学科建设项目资助.

Tang Yuelong, Hua Yuchun. SUPERCONVERGENCE ANALYSIS OF SPLITTING POSITIVE DEFINITE MIXED FINITE ELEMENT FOR ELLIPTIC OPTIMAL CONTROL PROBLEM[J]. Mathematica Numerica Sinica, 2021, 43(4): 506-515.

### SUPERCONVERGENCE ANALYSIS OF SPLITTING POSITIVE DEFINITE MIXED FINITE ELEMENT FOR ELLIPTIC OPTIMAL CONTROL PROBLEM

Tang Yuelong, Hua Yuchun

1. Hunan University of Science and Engineering, Yongzhou 425199, China
• Received:2020-06-30 Online:2021-11-14 Published:2021-11-12

Firstly, we use variational principle and optimization theory to obtain the equivalent optimality conditions of the original problem. Secondly, we construct a splitting positive definite mixed finite element approximation scheme for the elliptic optimal control problem. Thirdly, by introducing some important intermediate variables and projection operator and utilizing their properties, we derive the superconvergence based on the approximation properties of splitting positive definite mixed finite element method. Finally, a numerical example is provided to validate our theoretical results.

MR(2010)主题分类:

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