On finite element error estimates for optimal control problems with elliptic PDEs

Authors:
Fredi Tröltzsch
Affiliations:
Institut für Mathematik, Technische Universität Berlin, Berlin, Germany
Venue:
LSSC'09 Proceedings of the 7th international conference on Large-Scale Scientific Computing
Year:
2009

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Abstract

Discretizations of optimal control problems for elliptic equations by finite element methods are considered The problems are subject to constraints on the control and may also contain pointwise state constraints Some techniques are surveyed to estimate the distance between the exact optimal control and the associated optimal control of the discretized problem As a particular example, an error estimate for a nonlinear optimal control problem with finitely many control values and state constraints in finitely many points of the spatial domain is derived.