TY - JOUR
T1 - Discontinuous Galerkin Approximations for Distributed Optimal Control Problems Constrained by Parabolic PDE's
AU - Chrysafinos , Konstantinos
JO - International Journal of Numerical Analysis and Modeling
VL - 3-4
SP - 690
EP - 712
PY - 2007
DA - 2007/04
SN - 4
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/884.html
KW - error estimates, discontinuous Galerkin, optimal control, parabolic PDE's, distributed control, convection dominated, convection-diffusion equations.
AB - <p style="text-align: justify;">A discontinuous Galerkin finite element method for optimal control
problems having states constrained by linear parabolic PDE&#39;s is examined. The
spacial operator may depend on time and need not be self-adjoint. The schemes
considered here are discontinuous in time but conforming in space. 
Fully-discrete error estimates of arbitrary order are presented and various constants
are tracked. In particular, the estimates are valid for small values of $\alpha$, $\gamma$, where $\alpha$ denotes the penalty parameter of the cost functional and $\gamma$&nbsp; the coercivity
constant. Finally, error estimates for the convection dominated 
convection-diffusion equation are presented, based on a Lagrangian moving mesh approach.</p>