A CHARACTERISTIC MIXED FINITE ELEMENT METHOD FOR BILINEAR CONVECTION-DIFFUSION OPTIMAL CONTROL PROBLEMS

被引：2
作者：
Tang, Yuelong [1 ]
机构：
[1] Hunan Univ Sci & Engn, Coll Sci, Yongzhou 425100, Peoples R China
来源：
JOURNAL OF NONLINEAR FUNCTIONAL ANALYSIS | 2022年 / 2022卷
基金：
中国国家自然科学基金;
关键词：
A priori error estimates; Bilinear convection-diffusion optimal control problems; Characteristic mixed finite element methods; APPROXIMATION;
D O I：
10.23952/jnfa.2022.39
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we investigate a fully discrete characteristic mixed finite element approximation of bilinear convection-diffusion optimal control problems. The characteristic line method and backward difference are used for the time discretization. The lowest order Raviart-Thomas mixed finite element method is used for the space discretization. A priori error estimates for both the control and state numerical solutions are derived. Theoretical results are confirmed by a numerical example.
引用
收藏
页数：14
相关论文
共 29 条
[21]   L∞-error estimates of rectangular mixed finite element methods for bilinear optimal control problem [J].
Lu, Zuliang ;
Zhang, Shuhua .
APPLIED MATHEMATICS AND COMPUTATION, 2017, 300 :79-94
[22]   A stable Gaussian radial basis function method for solving nonlinear unsteady convection-diffusion-reaction equations [J].
Rashidinia, J. ;
Khasi, M. ;
Fasshauer, G. E. .
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2018, 75 (05) :1831-1850
[23]   A second order characteristic finite element scheme for convection-diffusion problems [J].
Rui, HX ;
Tabata, M .
NUMERISCHE MATHEMATIK, 2002, 92 (01) :161-177
[24]   A numerical method based on a bilinear pseudo-spectral method to solve the convection-diffusion optimal control problems [J].
Samadi, Fereshteh ;
Heydari, Aghileh ;
Effati, Sohrab .
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2021, 98 (01) :28-46
[25]   Adaptive variational discretization approximation method for parabolic optimal control problems [J].
Tang, Yuelong ;
Hua, Yuchun .
JOURNAL OF INEQUALITIES AND APPLICATIONS, 2020, 2020 (01)
[26]   A novel radial basis function method for 3D linear and nonlinear advection diffusion reaction equations with variable coefficients [J].
Tian, Xia ;
Lin, Ji .
ENGINEERING WITH COMPUTERS, 2022, 38 (SUPPL 1) :475-488
[27]   Numerical simulations for the chemotaxis models on surfaces via a novel characteristic finite element method [J].
Xiao, Xufeng ;
Feng, Xinlong ;
He, Yinnian .
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2019, 78 (01) :20-34
[28]   Error estimates of mixed methods for optimal control problems governed by parabolic equations [J].
Xing, Xaoqing ;
Chen, Yanping .
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 2008, 75 (06) :735-754
[29]   A discontinuous Galerkin method for optimal control problems governed by a system of convection-diffusion PDEs with nonlinear reaction terms [J].
Yuecel, Hamdullah ;
Stoll, Martin ;
Benner, Peter .
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2015, 70 (10) :2414-2431
123