A Robust Multigrid Method for Elliptic Optimal Control Problems

Authors:
Joachim Schöberl;René Simon;Walter Zulehner
Affiliations:
joachim.schoeberl@tuwien.ac.at;rene.simon@uni-due.de;zulehner@numa.uni-linz.ac.at
Venue:
SIAM Journal on Numerical Analysis
Year:
2011

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Abstract

We consider the discretized optimality system of a special class of elliptic optimal control problems and propose an all-at-once multigrid method for solving this discretized system. Under standard assumptions the convergence of the multigrid method and the robustness of the convergence rates with respect to the involved parameter are shown. Numerical experiments are presented for illustrating the theoretical results.