Abstract

AbstractIn this paper we investigate a space‐time finite element approximation of parabolic optimal control problems. The first order optimality conditions are transformed into an elliptic equation of fourth order in space and second order in time involving only the state or the adjoint state in the space‐time domain. We derive a priori and a posteriori error estimates for the time discretization of the state and the adjoint state. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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