A Priori Error Estimates of Mixed Finite Element Methods for General Linear Hyperbolic Convex Optimal Control Problems

被引：2
作者：
Lu, Zuliang [1 ,2 ]
Huang, Xiao [3 ]
机构：
[1] Chongqing Three Gorges Univ, Sch Math & Stat, Chongqing 404000, Peoples R China
[2] Beijing Computat Sci Res Ctr, Lab Appl Math, Beijing 100084, Peoples R China
[3] Chongqing Three Gorges Univ, Coll Elect & Informat Engn, Chongqing 404000, Peoples R China
来源：
ABSTRACT AND APPLIED ANALYSIS | 2014年
基金：
美国国家科学基金会;
关键词：
APPROXIMATION; SUPERCONVERGENCE; CONVERGENCE;
D O I：
10.1155/2014/547490
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The aim of this work is to investigate the discretization of general linear hyperbolic convex optimal control problems by using the mixed finite element methods. The state and costate are approximated by the k order (k >= 0) Raviart-Thomas mixed finite elements and the control is approximated by piecewise polynomials of order k. By applying the elliptic projection operators and Gronwall's lemma, we derive a priori error estimates of optimal order for both the coupled state and the control approximation.
引用
收藏
页数：10
相关论文
共 50 条
  • [21] Error Estimates of Variational Discretization and Mixed Finite Element Methods for Quasilinear Optimal Control Problems
    Lu, Zuliang
    Huang, Xiao
    PROCEEDINGS OF THE 2012 24TH CHINESE CONTROL AND DECISION CONFERENCE (CCDC), 2012, : 3519 - 3523
  • [22] 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
  • [23] Recovery Type A Posteriori Error Estimates of Fully Discrete Finite Element Methods for General Convex Parabolic Optimal Control Problems
    Tang, Yuelong
    Chen, Yanping
    NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS, 2012, 5 (04) : 573 - 591
  • [24] A priori error estimates of Crank-Nicolson finite element method for parabolic optimal control problems
    Zhang, Xindan
    Zhao, Jianping
    Hou, Yanren
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2023, 144 : 274 - 289
  • [25] Error estimates and superconvergence of a mixed finite element method for elliptic optimal control problems
    Hou, Tianliang
    Liu, Chunmei
    Yang, Yin
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2017, 74 (04) : 714 - 726
  • [26] A POSTERIORI ERROR ESTIMATES OF TRIANGULAR MIXED FINITE ELEMENT METHODS FOR QUADRATIC CONVECTION DIFFUSION OPTIMAL CONTROL PROBLEMS
    Lu, Z.
    MATHEMATICAL REPORTS, 2016, 18 (03): : 335 - 354
  • [27] ERROR ESTIMATES OF FINITE VOLUME ELEMENT METHOD FOR NONLINEAR HYPERBOLIC OPTIMAL CONTROL PROBLEMS
    Lu, Zuliang
    Li, Lin
    Feng, Yuming
    Cao, Longzhou
    Zhang, Wei
    ITALIAN JOURNAL OF PURE AND APPLIED MATHEMATICS, 2019, (41): : 70 - 84
  • [28] A Priori Error Estimates and Superconvergence of P02-P1 Mixed Finite Element Methods for Elliptic Boundary Control Problems
    Xu, Ch.
    NUMERICAL ANALYSIS AND APPLICATIONS, 2021, 14 (01) : 55 - 68
  • [29] Superconvergence and a posteriori error estimates of splitting positive definite mixed finite element methods for elliptic optimal control problems
    Hou, Tianliang
    Li, Li
    APPLIED MATHEMATICS AND COMPUTATION, 2016, 273 : 1196 - 1207
  • [30] L∞-error estimates of rectangular mixed finite element methods for bilinear optimal control problem
    Lu, Zuliang
    Zhang, Shuhua
    APPLIED MATHEMATICS AND COMPUTATION, 2017, 300 : 79 - 94
12345