@Article{JCM-33-158,
author = {Hou , Tianliang and Chen , Yanping},
title = {Mixed Discontinuous Galerkin Time-Stepping Method for Linear Parabolic Optimal Control Problems},
journal = {Journal of Computational Mathematics},
year = {2015},
volume = {33},
number = {2},
pages = {158--178},
abstract = {<p style="text-align: justify;">In this paper, we discuss the mixed discontinuous Galerkin (DG) finite element approximation to linear parabolic optimal control problems. For the state variables and the co-state variables, the discontinuous finite element method is used for the time discretization and the Raviart-Thomas mixed finite element method is used for the space discretization. We do not discretize the space of admissible control but implicitly utilize the relation between co-state and control for the discretization of the control. We derive a priori error estimates for the lowest order mixed DG finite element approximation. Moveover, for the element of arbitrary order in space and time, we derive a posteriori $L^2(0, T ;L^2(Ω))$ error estimates for the scalar functions, assuming that only the underlying mesh is static. Finally, we present an example to confirm the theoretical result on a priori error estimates.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.1211-m4267},
url = {http://global-sci.org/intro/article_detail/jcm/9834.html}
}