Darcy方程最优控制问题的混合虚拟单元方法的先验误差分析

IF 1.1 4区数学 Q2 MATHEMATICS, APPLIED East Asian Journal on Applied Mathematics Pub Date : 2023-06-01 DOI:10.4208/eajam.070322.210722

Xiuhe Wang, Qiming Wang null, Zhaojie Zhou

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引用次数: 2

摘要

．研究了带点控制约束的达西方程最优控制问题的混合虚元离散化问题。离散方案使用状态方程的虚元近似和控制变量的变分离散化。采用先离散后优化的方法，得到一个离散的一阶最优系统。推导了状态变量、联合变量和控制变量的先验误差估计。数值实验证实了理论结果。

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A Priori Error Analysis of Mixed Virtual Element Methods for Optimal Control Problems Governed by Darcy Equation

. A mixed virtual element discretization of optimal control problems governed by the Darcy equation with pointwise control constraint is investigated. A discrete scheme uses virtual element approximations of the state equation and a variational discretization of the control variable. A discrete ﬁrst-order optimality system is obtained by the ﬁrst-discretize-then-optimize approach. A priori error estimates of the state, ad-joint, and control variables are derived. Numerical experiments conﬁrm the theoretical results.

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来源期刊

East Asian Journal on Applied Mathematics MATHEMATICS, APPLIED-

CiteScore

2.60

自引率

8.30%

发文量

期刊介绍： The East Asian Journal on Applied Mathematics (EAJAM) aims at promoting study and research in Applied Mathematics in East Asia. It is the editorial policy of EAJAM to accept refereed papers in all active areas of Applied Mathematics and related Mathematical Sciences. Novel applications of Mathematics in real situations are especially welcome. Substantial survey papers on topics of exceptional interest will also be published occasionally.