New a posteriori error estimates for hp version of finite element methods of nonlinear parabolic optimal control problems

被引：0
|
作者：
Zuliang Lu
Hongyan Liu
Chunjuan Hou
Longzhou Cao
机构：
[1] Chongqing Three Gorges University,Key Laboratory of Signal and Information Processing
[2] Chongqing Three Gorges University,Key Laboratory for Nonlinear Science and System Structure
[3] Tianjin University of Finance and Economics,Research Center for Mathematics and Economics
[4] Chongqing Wanzhou Long Bao Middle School,Huashang College
[5] Guangdong University of Finance,undefined
来源：
Journal of Inequalities and Applications | / 2016卷
关键词：
residual-based ; error estimates; nonlinear parabolic optimal control problems; version of finite element method; 49J20; 65N30;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, we investigate residual-based a posteriori error estimates for the hp version of the finite element approximation of nonlinear parabolic optimal control problems. By using the hp finite element approximation for both the state and the co-state variables and the hp discontinuous Galerkin finite element approximation for the control variable, we derive hp residual-based a posteriori error estimates for both the state and the control approximation. Such estimates, which are apparently not available in the literature, can be used to construct a reliable hp adaptive finite element approximation for the nonlinear parabolic optimal control problems.
引用
收藏
相关论文
共 50 条
  • [1] New a posteriori error estimates for hp version of finite element methods of nonlinear parabolic optimal control problems
    Lu, Zuliang
    Liu, Hongyan
    Hou, Chunjuan
    Cao, Longzhou
    JOURNAL OF INEQUALITIES AND APPLICATIONS, 2016, : 1 - 17
  • [2] A Posteriori Error Estimates of Semidiscrete Mixed Finite Element Methods for Parabolic Optimal Control Problems
    Chen, Yanping
    Lin, Zhuoqing
    EAST ASIAN JOURNAL ON APPLIED MATHEMATICS, 2015, 5 (01) : 85 - 108
  • [3] A posteriori error estimates of hp spectral element method for parabolic optimal control problems
    Lu, Zuliang
    Cai, Fei
    Xu, Ruixiang
    Hou, Chunjuan
    Wu, Xiankui
    Yang, Yin
    AIMS MATHEMATICS, 2022, 7 (04): : 5220 - 5240
  • [4] A posteriori error estimates for hp finite element solutions of convex optimal control problems
    Chen, Yanping
    Lin, Yijie
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2011, 235 (12) : 3435 - 3454
  • [5] A POSTERIORI ERROR ESTIMATES OF MIXED METHODS FOR PARABOLIC OPTIMAL CONTROL PROBLEMS
    Chen, Yanping
    Liu, Lingli
    Lu, Zuliang
    NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2010, 31 (10) : 1135 - 1157
  • [6] A posteriori error estimates of the weak Galerkin finite element methods for parabolic problems
    Dai, Jiajia
    Chen, Luoping
    Yang, Miao
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2024, 445
  • [7] A posteriori error estimates of finite element method for parabolic problems
    Chen, YP
    ACTA MATHEMATICA SCIENTIA, 1999, 19 (04) : 449 - 456
  • [8] A posteriori L∞(L∞)-error estimates for finite-element approximations to parabolic optimal control problems
    Manohar, Ram
    Sinha, Rajen Kumar
    COMPUTATIONAL & APPLIED MATHEMATICS, 2021, 40 (08):
  • [9] A posteriori error estimates for mixed finite element approximation of nonlinear quadratic optimal control problems
    Chen, Yanping
    Lu, Zuliang
    Fu, Min
    OPTIMIZATION METHODS & SOFTWARE, 2013, 28 (01): : 37 - 53
  • [10] A posteriori error estimates of finite element methods for nonlinear quadratic boundary optimal control problem
    Lu Z.
    Numerical Analysis and Applications, 2011, 4 (3) : 210 - 222
12345