Volume 44, Number 1, January-February 2010
|Page(s)||189 - 206|
|Published online||16 December 2009|
Convergence of discontinuous Galerkin approximations of an optimal control problem associated to semilinear parabolic PDE's
National Technical University of
Athens, Department of Mathematics, Zografou Campus, Athens 15780,
Revised: 15 July 2009
A discontinuous Galerkin finite element method for an optimal control problem related to semilinear parabolic PDE's is examined. The schemes under consideration are discontinuous in time but conforming in space. Convergence of discrete schemes of arbitrary order is proven. In addition, the convergence of discontinuous Galerkin approximations of the associated optimality system to the solutions of the continuous optimality system is shown. The proof is based on stability estimates at arbitrary time points under minimal regularity assumptions, and a discrete compactness argument for discontinuous Galerkin schemes (see Walkington [SINUM (June 2008) (submitted), preprint available at http://www.math.cmu.edu/~noelw], Sects. 3, 4).
Mathematics Subject Classification: 65M60 / 49J20
Key words: Discontinuous Galerkin approximations / distributed controls / stability estimates / semi-linear parabolic PDE's.
© EDP Sciences, SMAI, 2009
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.