@Article{JCM-42-1579,
author = {Shakya , Pratibha},
title = {Error Analysis for Parabolic Optimal Control Problems with Measure Data in a Nonconvex Polygonal Domain},
journal = {Journal of Computational Mathematics},
year = {2024},
volume = {42},
number = {6},
pages = {1579--1604},
abstract = {<p style="text-align: justify;">This paper considers the finite element approximation to parabolic optimal control
problems with measure data in a nonconvex polygonal domain. Such problems usually
possess low regularity in the state variable due to the presence of measure data and the
nonconvex nature of the domain. The low regularity of the solution allows the finite
element approximations to converge at lower orders. We prove the existence, uniqueness
and regularity results for the solution to the control problem satisfying the first order
optimality condition. For our error analysis we have used piecewise linear elements for the
approximation of the state and co-state variables, whereas piecewise constant functions
are employed to approximate the control variable. The temporal discretization is based on
the implicit Euler scheme. We derive both a priori and a posteriori error bounds for the
state, control and co-state variables. Numerical experiments are performed to validate the
theoretical rates of convergence.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.2305-m2022-0215},
url = {http://global-sci.org/intro/article_detail/jcm/23508.html}
}