Year: 2012
Numerical Mathematics: Theory, Methods and Applications, Vol. 5 (2012), Iss. 1 : pp. 1–18
Abstract
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.
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.2011.m12si01
Numerical Mathematics: Theory, Methods and Applications, Vol. 5 (2012), Iss. 1 : pp. 1–18
Published online: 2012-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Keywords: Multigrid methods Lavrentiev regularization semismooth Newton methods parabolic partial differential equations optimal control theory.