Loading [MathJax]/jax/output/CommonHTML/jax.js
Journals
Resources
About Us
Open Access
Go to previous page

A Priori Error Estimates of Finite Element Methods for Linear Parabolic Integro-Differential Optimal Control Problems

A Priori Error Estimates of Finite Element Methods for Linear Parabolic Integro-Differential Optimal Control Problems

Year:    2014

Author:    Wanfang Shen, Liang Ge, Danping Yang, Wenbin Liu

Advances in Applied Mathematics and Mechanics, Vol. 6 (2014), Iss. 5 : pp. 552–569

Abstract

In this paper, we study the mathematical formulation for an optimal control problem governed by a linear parabolic integro-differential equation and present the optimality conditions. We then set up its weak formulation and the finite element approximation scheme. Based on these we derive the a priori error estimates for its finite element approximation both in H1 and L2 norms. Furthermore, some numerical tests are presented to verify the theoretical results.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.2012.m30

Advances in Applied Mathematics and Mechanics, Vol. 6 (2014), Iss. 5 : pp. 552–569

Published online:    2014-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    18

Keywords:    Optimal control linear parabolic integro-differential equations optimality conditions finite element methods a priori error estimate.

Author Details

Wanfang Shen Email

Liang Ge Email

Danping Yang Email

Wenbin Liu Email

  1. L ∞ -error estimates of rectangular mixed finite element methods for bilinear optimal control problem

    Lu, Zuliang | Zhang, Shuhua

    Applied Mathematics and Computation, Vol. 300 (2017), Iss. P.79

    https://doi.org/10.1016/j.amc.2016.12.006 [Citations: 9]
  2. Sharp A Posteriori Error Estimates for Optimal Control Governed by Parabolic Integro-Differential Equations

    Shen, Wanfang | Ge, Liang | Yang, Danping | Liu, Wenbin

    Journal of Scientific Computing, Vol. 65 (2015), Iss. 1 P.1

    https://doi.org/10.1007/s10915-014-9957-3 [Citations: 12]
  3. A stabilizer-free weak Galerkin finite element method for an optimal control problem of a time fractional diffusion equation

    Wang, Shuo | Ma, Jie | Du, Ning

    Mathematics and Computers in Simulation, Vol. 231 (2025), Iss. P.99

    https://doi.org/10.1016/j.matcom.2024.11.019 [Citations: 0]
  4. Finite element method for an optimal control problem governed by a time fractional wave equation

    Wang, Shuo | Zheng, Xiangcheng | Du, Ning

    Computers & Mathematics with Applications, Vol. 164 (2024), Iss. P.45

    https://doi.org/10.1016/j.camwa.2024.03.034 [Citations: 0]
  5. Full-discrete adaptive FEM for quasi-parabolic integro-differential PDE-constrained optimal control problem

    Shen, Wanfang

    Boundary Value Problems, Vol. 2016 (2016), Iss. 1

    https://doi.org/10.1186/s13661-016-0626-3 [Citations: 0]