时间周期涡流问题最优控制的后验误差估计

IF 1 4区数学 Q3 MATHEMATICS, APPLIED

Computational Methods in Applied Mathematics Pub Date : 2023-11-27 DOI:10.1515/cmam-2023-0119

Monika Wolfmayr

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引用次数: 1

摘要

本文提出了分布式涡流最优控制问题的泛函型后验估计的多谐分析和推导及其在时间周期设置下的状态方程。通过推导出最优系统和正问题的一个弱空时变分公式解的存在唯一性，证明了其存在唯一性。利用if -sup和sup-sup条件，在函数型后验估计框架下，导出了最优控制问题和正演问题的近似误差的保证、尖锐和完全可计算的界。在这里，我们给出了推导估计的第一个计算结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A Posteriori Error Estimation for the Optimal Control of Time-Periodic Eddy Current Problems

This work presents the multiharmonic analysis and derivation of functional type a posteriori estimates of a distributed eddy current optimal control problem and its state equation in a time-periodic setting. The existence and uniqueness of the solution of a weak space-time variational formulation for the optimality system and the forward problem are proved by deriving inf-sup and sup-sup conditions. Using the inf-sup and sup-sup conditions, we derive guaranteed, sharp and fully computable bounds of the approximation error for the optimal control problem and the forward problem in the functional type a posteriori estimation framework. We present here the first computational results on the derived estimates.

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来源期刊

Computational Methods in Applied Mathematics MATHEMATICS, APPLIED-

CiteScore

2.40

自引率

7.70%

发文量

期刊介绍： The highly selective international mathematical journal Computational Methods in Applied Mathematics　(CMAM) considers original mathematical contributions to computational methods and numerical analysis with applications mainly related to PDEs. CMAM seeks to be interdisciplinary while retaining the common thread of numerical analysis, it is intended to be readily readable and meant for a wide circle of researchers in applied mathematics. The journal is published by De Gruyter on behalf of the Institute of Mathematics of the National Academy of Science of Belarus.