三维点跟踪Stokes问题最优控制的改进误差估计

IF 1 4区数学 Q1 MATHEMATICS

Mathematical Control and Related Fields Pub Date : 2021-01-01 DOI:10.3934/mcrf.2020038

Niklas Behringer

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引用次数: 2

摘要

．这项工作的动机是最近对Stokes问题的点跟踪型最优控制问题的主题感兴趣。点跟踪由目标函数中的点评估组成，这导致狄拉克测度作为伴随问题的源项出现。考虑控制的边界可以改善精确解的正则性结果，并改善其数值对应物的近似误差估计。我们在三个维度上展示了次优收敛结果，尽管如此，它改善了文献中已知的结果。最后，我们提供了支持数值实验和对最优逼近误差估计的见解。

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Improved error estimates for optimal control of the Stokes problem with pointwise tracking in three dimensions

. This work is motivated by recent interest in the topic of pointwise tracking type optimal control problems for the Stokes problem. Pointwise tracking consists of point evaluations in the objective functional which lead to Dirac measures appearing as source terms of the adjoint problem. Consider- ing bounds for the control allows for improved regularity results for the exact solution and improved approximation error estimates of its numerical coun- terpart. We show a sub-optimal convergence result in three dimensions that nonetheless improves the results known from the literature. Finally, we oﬀer supporting numerical experiments and insights towards optimal approximation error estimates.

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来源期刊

Mathematical Control and Related Fields MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.50

自引率

8.30%

发文量

期刊介绍： MCRF aims to publish original research as well as expository papers on mathematical control theory and related fields. The goal is to provide a complete and reliable source of mathematical methods and results in this field. The journal will also accept papers from some related fields such as differential equations, functional analysis, probability theory and stochastic analysis, inverse problems, optimization, numerical computation, mathematical finance, information theory, game theory, system theory, etc., provided that they have some intrinsic connections with control theory.