Error estimates of finite volume method for Stokes optimal control problem

被引：2

作者：

Lan, Lin ^{[1
]}

Chen, Ri-hui ^{[1
]}

Wang, Xiao-dong ^{[1
]}

Ma, Chen-xia ^{[1
]}

Fu, Hao-nan ^{[1
]}

机构：

[1] Kunming Univ Sci & Technol, Fac Land Resources Engn, Kunming 650093, Yunnan, Peoples R China

来源：

JOURNAL OF INEQUALITIES AND APPLICATIONS | 2021年 / 2021卷 / 01期

关键词：

Optimal control problem; Stokes equations; Finite volume method; A priori error estimates; Variational discretization; 49J20; 65N30; UNIFIED ANALYSIS; ELEMENT METHODS; APPROXIMATION; OPTIMIZATION;

D O I：

10.1186/s13660-020-02532-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we discuss a priori error estimates for the finite volume element approximation of optimal control problem governed by Stokes equations. Under some reasonable assumptions, we obtain optimal L2-norm error estimates. The approximate orders for the state, costate, and control variables are O(h2) in the sense of L2-norm. Furthermore, we derive H1-norm error estimates for the state and costate variables. Finally, we give some conclusions and future works.

引用

页数：13

共 50 条

[31] A Posteriori Error Estimates for the Virtual Element Method for the Stokes Problem
Gang Wang
Ying Wang
Yinnian He
[J]. Journal of Scientific Computing, 2020, 84
[32] A posteriori error estimates of spectral method for nonlinear parabolic optimal control problem
Li, Lin
Lu, Zuliang
Zhang, Wei
Huang, Fei
Yang, Yin
[J]. JOURNAL OF INEQUALITIES AND APPLICATIONS, 2018,
[33] A posteriori error estimates of spectral method for nonlinear parabolic optimal control problem
Lin Li
Zuliang Lu
Wei Zhang
Fei Huang
Yin Yang
[J]. Journal of Inequalities and Applications, 2018
[34] Analysis of a finite volume element method for the Stokes problem
Alfio Quarteroni
Ricardo Ruiz-Baier
[J]. Numerische Mathematik, 2011, 118 : 737 - 764
[35] Analysis of a finite volume element method for the Stokes problem
Quarteroni, Alfio
Ruiz-Baier, Ricardo
[J]. NUMERISCHE MATHEMATIK, 2011, 118 (04) : 737 - 764
[36] An optimal adaptive finite element method for the Stokes problem
Kondratyuk, Yaroslav
Stevenson, Rob
[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 2008, 46 (02) : 747 - 775
[37] The Optimal Error Estimate of the Fully Discrete Locally Stabilized Finite Volume Method for the Non-Stationary Navier-Stokes Problem
He, Guoliang
Zhang, Yong
[J]. ENTROPY, 2022, 24 (06)
[38] Error Estimates for the Heterogeneous Multiscale Finite Volume Method of Convection-Diffusion-Reaction Problem
Yu, Tao
Ouyang, Peichang
Cao, Haitao
[J]. COMPLEXITY, 2018,
[39] Error estimates and superconvergence of a mixed finite element method for elliptic optimal control problems
Hou, Tianliang
Liu, Chunmei
Yang, Yin
[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2017, 74 (04) : 714 - 726
[40] POINTWISE ERROR ESTIMATES OF FINITE ELEMENT APPROXIMATIONS TO THE STOKES PROBLEM ON CONVEX POLYHEDRA
Guzman, J.
Leykekhman, D.
[J]. MATHEMATICS OF COMPUTATION, 2012, 81 (280) : 1879 - 1902

← 1 2 3 4 5 →