@Article{CiCP-18-621,
author = {},
title = {Boundary Control Problems in Convective Heat Transfer with Lifting Function Approach and Multigrid Vanka-Type Solvers},
journal = {Communications in Computational Physics},
year = {2018},
volume = {18},
number = {3},
pages = {621--649},
abstract = {<p style="text-align: justify;">This paper deals with boundary optimal control problems for the heat and
Navier-Stokes equations and addresses the issue of defining controls in function spaces
which are naturally associated with the volume variables by trace restriction. For this
reason we reformulate the boundary optimal control problem into a distributed problem
through a lifting function approach. The stronger regularity requirements which
are imposed by standard boundary control approaches can then be avoided. Furthermore,
we propose a new numerical strategy that allows solving the coupled optimality
system in a robust way for a large number of unknowns. The optimality system
resulting from a finite element discretization is solved by a local multigrid algorithm
with domain decomposition Vanka-type smoothers. The purpose of these smoothers
is to solve the optimality system implicitly over subdomains with a small number of
degrees of freedom, in order to achieve robustness with respect to the regularization
parameters in the cost functional. We present the results of some test cases where temperature
is the observed quantity and the control quantity corresponds to the boundary
values of the fluid temperature in a portion of the boundary. The control region for
the observed quantity is a part of the domain where it is interesting to match a desired
temperature value.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.130914.230115a},
url = {http://global-sci.org/intro/article_detail/cicp/11043.html}
}