Full-discrete adaptive FEM for quasi-parabolic integro-differential PDE-constrained optimal control problem

Boundary value problems

Wanfang Shen¹ 

[1] School of Mathematic and Quantitative Economics, Shandong University of Finance and Economics, Jinan, China

关键词: full-discrete adaptive FEM;    equivalent a posteriori error estimates;    linear quasi-parabolic integro-differential PDE;    optimal control problem;    optimality conditions;    constrained control;   

DOI  :  10.1186/s13661-016-0626-3

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we develop a full-discrete adaptive FEM for a quasi-parabolic integro-differential PDE-constrained optimal control problem. Firstly, we present weak formulations and optimal conditions and, by using the backward Euler scheme, we deduce equivalent a posteriori error estimators. Then we derive lower and upper bounds for the error estimates by bubble function techniques and use these indicators in adaptive finite element schemes. Furthermore, we carry out some numerical experiments to test our theoretical results.

【 授权许可】

CC BY