L2(Γ) 中具有边界观测的椭圆最优控制问题的混合虚拟元素方法

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED Applied Numerical Mathematics Pub Date : 2024-05-24 DOI:10.1016/j.apnum.2024.05.019

Minghui Yang, Zhaojie Zhou

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引用次数: 0

摘要

本文研究了具有边界观测的椭圆最优控制问题的混合虚元近似。这类最优控制问题的目标函数包含边界上状态变量的外向法导数，这降低了最优控制问题解的正则性。我们构建了混合虚元离散方案，并根据控制变量的变分离散化推导出最优控制问题的先验误差估计。我们在不同网格上进行了数值实验，以支持我们的理论发现。

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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Mixed virtual element methods for elliptic optimal control problems with boundary observations in L2(Γ)

In this paper, we study the mixed virtual element approximation to an elliptic optimal control problem with boundary observations. The objective functional of this type of optimal control problem contains the outward normal derivatives of the state variable on the boundary, which reduces the regularity of solutions to the optimal control problems. We construct the mixed virtual element discrete scheme and derive an a priori error estimate for the optimal control problem based on the variational discretization for the control variable. Numerical experiments are carried out on different meshes to support our theoretical findings.

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来源期刊

Applied Numerical Mathematics 数学-应用数学

CiteScore

5.60

自引率

7.10%

发文量

225

审稿时长

7.2 months

期刊介绍： The purpose of the journal is to provide a forum for the publication of high quality research and tutorial papers in computational mathematics. In addition to the traditional issues and problems in numerical analysis, the journal also publishes papers describing relevant applications in such fields as physics, fluid dynamics, engineering and other branches of applied science with a computational mathematics component. The journal strives to be flexible in the type of papers it publishes and their format. Equally desirable are: (i) Full papers, which should be complete and relatively self-contained original contributions with an introduction that can be understood by the broad computational mathematics community. Both rigorous and heuristic styles are acceptable. Of particular interest are papers about new areas of research, in which other than strictly mathematical arguments may be important in establishing a basis for further developments. (ii) Tutorial review papers, covering some of the important issues in Numerical Mathematics, Scientific Computing and their Applications. The journal will occasionally publish contributions which are larger than the usual format for regular papers. (iii) Short notes, which present specific new results and techniques in a brief communication.