宾厄姆型流体变分-半变量不等式的逼近和优化控制

IF 2.6 3区数学 Computational and Applied Mathematics Pub Date : 2024-09-12 DOI:10.1007/s40314-024-02787-3

Zakaria Faiz, Hicham Benaissa

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引用次数: 0

摘要

本文旨在研究有界域中的宾厄姆不可压缩流体模型。我们得到了不可压缩流体模型的变分公式，即变分-半变量不等式。利用半变量不等式理论的最新进展，证明了解的存在性和唯一性。此外，我们还利用有限元法分析了模型的完全离散近似值，并提供了近似解的误差估计。最后，我们证明了连续依赖性结果，并建立了宾厄姆型不可压缩流体的最优对。

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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Approximation and optimal control for variational–hemivariational inequalities of Bingham type fluid

The aim of this paper is to investigate a model of incompressible fluid of Bingham type in a bounded domain. We obtain the variational formulation of the model of incompressible fluid which is a variational–hemivariational inequality. The existence and uniqueness of the solution are proven utilizing recent advancements in the theory of hemivariational inequalities. Additionally, employing the finite element method, we analyze a fully discrete approximation of the model and provide error estimates for the approximate solutions. Finally, we demonstrate a continuous dependence result and establish the existence of optimal pairs for the incompressible fluid of Bingham type.

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来源期刊

Computational and Applied Mathematics MATHEMATICS, APPLIED-

自引率

11.50%

发文量

352

期刊介绍： Computational & Applied Mathematics began to be published in 1981. This journal was conceived as the main scientific publication of SBMAC (Brazilian Society of Computational and Applied Mathematics). The objective of the journal is the publication of original research in Applied and Computational Mathematics, with interfaces in Physics, Engineering, Chemistry, Biology, Operations Research, Statistics, Social Sciences and Economy. The journal has the usual quality standards of scientific international journals and we aim high level of contributions in terms of originality, depth and relevance.