A Priori and A Posteriori Error Estimates of Streamline Diffusion Finite Element Method for Optimal Control Problem Governed by Convection Dominated Diffusion Equation

被引：0

作者：

Yan, Ningning ^{[1
]}

Zhou, Zhaojie ^{[1
]}

机构：

[1] Chinese Acad Sci, LSEC, Inst Syst Sci, Acad Math & Syst Sci, Beijing 100080, Peoples R China

来源：

NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS | 2008年 / 1卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Constrained optimal control problem; convection dominated diffusion equation; streamline diffusion finite element method; a priori error estimate; a posteriori error estimate;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we investigate a streamline diffusion finite element approximation scheme for the constrained optimal control problem governed by linear convection dominated diffusion equations. We prove the existence and uniqueness of the discretized scheme. Then a priori and a posteriori error estimates are derived for the state, the co-state and the control. Three numerical examples are presented to illustrate our theoretical results.

引用

页码：297 / 320

页数：24

共 50 条

[31] A posteriori error estimates for discontinuous Galerkin approximation of non-stationary convection-diffusion optimal control problems [J].

Zhou, Zhaojie .

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2016, 93 (12) :2106-2123

[32] How accurate is the streamline diffusion finite element method? [J].

Zhou, GH .

MATHEMATICS OF COMPUTATION, 1997, 66 (217) :31-44

[33] A Priori and a Posteriori Error Estimates for H(div)-Elliptic Problem with Interior Penalty Method [J].

Zeng, Yuping ;

Chen, Jinru .

COMMUNICATIONS IN COMPUTATIONAL PHYSICS, 2013, 14 (03) :753-779

[34] The a Priori and a Posteriori Error Estimates of DG Method for the Steklov Eigenvalue Problem in Inverse Scattering [J].

Li, Yanjun ;

Bi, Hai ;

Yang, Yidu .

JOURNAL OF SCIENTIFIC COMPUTING, 2022, 91 (01)

[35] The a Priori and a Posteriori Error Estimates of DG Method for the Steklov Eigenvalue Problem in Inverse Scattering [J].

Yanjun Li ;

Hai Bi ;

Yidu Yang .

Journal of Scientific Computing, 2022, 91

[36] A priori and a posteriori error estimates of a space-time Petrov-Galerkin spectral method for time-fractional diffusion equation [J].

Tang, Bo ;

Mao, Wenting ;

Zeng, Zhankuan .

MATHEMATICS AND COMPUTERS IN SIMULATION, 2024, 219 :559-572

[37] A Priori Error Analysis of Mixed Virtual Element Methods for Optimal Control Problems Governed by Darcy Equation [J].

Wang, Xiuhe ;

Wang, Qiming ;

Zhou, Zhaojie .

EAST ASIAN JOURNAL ON APPLIED MATHEMATICS, 2023, 13 (01) :140-161

[38] A POSTERIORI ERROR ANALYSIS OF FINITE ELEMENT METHOD FOR LINEAR NONLOCAL DIFFUSION AND PERIDYNAMIC MODELS [J].

Du, Qiang ;

Ju, Lili ;

Tian, Li ;

Zhou, Kun .

MATHEMATICS OF COMPUTATION, 2013, 82 (284) :1889-1922

[39] A RT Mixed FEM/DG Scheme for Optimal Control Governed by Convection Diffusion Equations [J].

Ningning Yan ;

Zhaojie Zhou .

Journal of Scientific Computing, 2009, 41

[40] A RT Mixed FEM/DG Scheme for Optimal Control Governed by Convection Diffusion Equations [J].

Yan, Ningning ;

Zhou, Zhaojie .

JOURNAL OF SCIENTIFIC COMPUTING, 2009, 41 (02) :273-299

← 1 2 3 4 5 →