::title::Variational Discretization of Parabolic Control Problems in the Presence of Pointwise State Constraints
::author::1::Klaus Deckelnic
::author::2::Michael Hinze
::address::1::Institut f\"ur Analysis und Numerik, Otto--von--Guericke--Universit\"at Magdeburg, Universit\"atsplatz 2, 39106 Magdeburg, Germany
::address::2::Schwerpunkt Optimierung und Approximation, Universit\"at Hamburg, Bundesstra{\ss}e 55, 20146 Hamburg, Germany
::email::klaus.deckelnick@mathematik.uni-magdeburg.de, michael.hinze@uni-hamburg.de
::receive::Received 2009-9-23 Accepted 2010-4-30
::online::Available online 2010-9-20
::DOI::10.4208/jcm.1004-m3213
::keywords::Parabolic optimal control problem, State constraints,  Error estimates.
::ams::49J20, 49K20, 35B37.
::abstract::
We consider a parabolic optimal control problem with pointwise state constraints. 
The optimization problem is approximated by a discrete control problem based on a 
discretization of the state equation by linear finite elements in space and a 
discontinuous Galerkin scheme in time. Error bounds for control and state are 
obtained both in two and three space dimensions. These bounds follow from uniform 
estimates for the discretization error of the state under natural regularity requirements.