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

被引：7

作者：

Wang, Xiuhe ^{[1
]}

Wang, Qiming ^{[2
]}

Zhou, Zhaojie ^{[1
]}

机构：

[1] Shandong Normal Univ, Sch Math & Stat, Jinan 250014, Peoples R China

[2] Beijing Normal Univ, Sch Math Sci, Zhuhai 519087, Peoples R China

来源：

EAST ASIAN JOURNAL ON APPLIED MATHEMATICS | 2023年 / 13卷 / 01期

基金：

中国国家自然科学基金;

关键词：

A priori error estimate; mixed virtual element method; optimal control problem; APPROXIMATION;

D O I：

10.4208/eajam.070322.210722

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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, adjoint, and control variables are derived. Numerical experiments confirm the theoretical results.

引用

页码：140 / 161

页数：22

共 21 条

[1] A C1 virtual element method for an elliptic distributed optimal control problem with pointwise state constraints [J].

Brenner, Susanne C. ;

Sung, Li-Yeng ;

Tan, Zhiyu .

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2021, 31 (14) :2887-2906

[2] BASIC PRINCIPLES OF MIXED VIRTUAL ELEMENT METHODS [J].

Brezzi, F. ;

Falk, Richard S. ;

Marini, L. Donatella .

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 2014, 48 (04) :1227-1240

[3] A posteriori error estimates for mixed finite element solutions of convex optimal control problems [J].

Chen, Yanping ;

Liu, Wenbin .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2008, 211 (01) :76-89

[4] Error Estimates and Superconvergence of Mixed Finite Element Methods for Convex Optimal Control Problems [J].

Chen, Yanping ;

Huang, Yunqing ;

Liu, Wenbin ;

Yan, Ningning .

JOURNAL OF SCIENTIFIC COMPUTING, 2010, 42 (03) :382-403

[5]

da Veiga LB, 2016, NUMER MATH, V133, P303, DOI 10.1007/s00211-015-0746-1

[6] BASIC PRINCIPLES OF VIRTUAL ELEMENT METHODS [J].

da Veiga, L. Beirao ;

Brezzi, F. ;

Cangiani, A. ;

Manzini, G. ;

Marini, L. D. ;

Russo, A. .

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2013, 23 (01) :199-214

[7] MIXED VIRTUAL ELEMENT METHODS FOR GENERAL SECOND ORDER ELLIPTIC PROBLEMS ON POLYGONAL MESHES [J].

da Veiga, Lourenco Beirao ;

Brezzi, Franco ;

Marini, Luisa Donatella ;

Russo, Alessandro .

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 2016, 50 (03) :727-747

[8] Parallel solvers for virtual element discretizations of elliptic equations in mixed form [J].

Dassi, F. ;

Scacchi, S. .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2020, 79 (07) :1972-1989

[9] Convergence of a finite element approximation to a state-constrained elliptic control problem [J].

Deckelnick, Klaus ;

Hinze, Michael .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2007, 45 (05) :1937-1953

[10] Finite element approximation of elliptic control problems with constraints on the gradient [J].

Deckelnick, Klaus ;

Gunther, Andreas ;

Hinze, Michael .

NUMERISCHE MATHEMATIK, 2009, 111 (03) :335-350

← 1 2 3 →