TY - JOUR
T1 - Multigrid Solution of a Lavrentiev-Regularized State-Constrained Parabolic Control Problem
AU - Alfio Borzì & Sergio González Andrade
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 1
SP - 1
EP - 18
PY - 2012
DA - 2012/05
SN - 5
DO - http://doi.org/10.4208/nmtma.2011.m12si01
UR - https://global-sci.org/intro/article_detail/nmtma/5925.html
KW - Multigrid methods, Lavrentiev regularization, semismooth Newton methods, parabolic
partial differential equations, optimal control theory.
AB - <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>