@Article{NMTMA-5-1,
author = {Alfio Borzì and Sergio González Andrade},
title = {Multigrid Solution of a Lavrentiev-Regularized State-Constrained Parabolic Control Problem},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2012},
volume = {5},
number = {1},
pages = {1--18},
abstract = {<p style="text-align: justify;">A mesh-independent, robust, and accurate multigrid scheme to solve a linear state-constrained
parabolic optimal control problem is presented. We first consider a Lavrentiev regularization of the
state-constrained optimization problem. Then, a multigrid scheme is designed for the numerical
solution of the regularized optimality system. Central to this scheme is the construction of an
iterative pointwise smoother which can be formulated as a local semismooth Newton iteration. Results
of numerical experiments and theoretical two-grid local Fourier analysis estimates demonstrate that
the proposed scheme is able to solve parabolic state-constrained optimality systems with textbook
multigrid efficiency.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.2011.m12si01},
url = {http://global-sci.org/intro/article_detail/nmtma/5925.html}
}