Space-time finite element methods for parabolic distributed optimal control problems
Numerical Analysis
2022-08-23 v1 Numerical Analysis
Optimization and Control
Abstract
We present a method for the numerical approximation of distributed optimal control problems constrained by parabolic partial differential equations. We complement the first-order optimality condition by a recently developed space-time variational formulation of parabolic equations which is coercive in the energy norm, and a Lagrangian multiplier. Our final formulation fulfills the Babu\v{s}ka-Brezzi conditions on the continuous as well as discrete level, without restrictions. Consequently, we can allow for final-time desired states, and obtain an a-posteriori error estimator which is efficient and reliable. Numerical experiments confirm our theoretical findings.
Cite
@article{arxiv.2208.09879,
title = {Space-time finite element methods for parabolic distributed optimal control problems},
author = {Thomas Führer and Michael Karkulik},
journal= {arXiv preprint arXiv:2208.09879},
year = {2022}
}