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finitely many pointwise state constraints

ESAIM: Mathematical Modelling and Numerical Analysis (1)

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Error estimates for the finite element approximationof a semilinear elliptic control problem with state constraints and finite dimensional control space
Pedro Merino, Fredi Tröltzsch, Boris Vexler
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 44 / Issue 1 / January 2010

Published online by Cambridge University Press:

16 December 2009, pp. 167-188

Print publication:

January 2010
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The finite element approximation of optimal control problems forsemilinear elliptic partial differential equation is considered,where the control belongs to a finite-dimensional set and stateconstraints are given in finitely many points of the domain. Underthe standard linear independency condition on the active gradientsand a strong second-order sufficient optimality condition, optimalerror estimates are derived for locally optimal controls.