@Article{AAMM-6-552,
author = {Wanfang Shen, Liang Ge, Danping Yang and Wenbin Liu},
title = {A Priori Error Estimates of Finite Element Methods for Linear Parabolic Integro-Differential Optimal Control Problems},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2014},
volume = {6},
number = {5},
pages = {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 $H^1$ and $L^2$ norms. Furthermore
some numerical tests are presented to
verify the theoretical results.
},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.2012.m30},
url = {http://global-sci.org/intro/article_detail/aamm/35.html}
}
TY - JOUR
T1 - A Priori Error Estimates of Finite Element Methods for Linear Parabolic Integro-Differential Optimal Control Problems
AU - Wanfang Shen, Liang Ge, Danping Yang & Wenbin Liu
JO - Advances in Applied Mathematics and Mechanics
VL - 5
SP - 552
EP - 569
PY - 2014
DA - 2014/06
SN - 6
DO - http://dor.org/10.4208/aamm.2012.m30
UR - https://global-sci.org/intro/aamm/35.html
KW - Optimal control
KW - linear parabolic integro-differential equations
KW - optimality conditions
KW - finite element methods
KW - a priori error estimate
AB -
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 $H^1$ and $L^2$ norms. Furthermore
some numerical tests are presented to
verify the theoretical results.
Wanfang Shen, Liang Ge, Danping Yang & Wenbin Liu. (1970). A Priori Error Estimates of Finite Element Methods for Linear Parabolic Integro-Differential Optimal Control Problems.
Advances in Applied Mathematics and Mechanics. 6 (5).
552-569.
doi:10.4208/aamm.2012.m30
