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Convergence of discontinuous Galerkinapproximationsof an optimal control problem associatedtosemilinear parabolic PDE's

Published online by Cambridge University Press:  16 December 2009

Konstantinos Chrysafinos
Konstantinos Chrysafinos*
Affiliation:
National Technical University of Athens, Department of Mathematics, Zografou Campus, Athens 15780, Greece. chrysafinos@math.ntua.gr
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Abstract

A discontinuous Galerkin finite element method for an optimalcontrol problem related to semilinear parabolic PDE's is examined.The schemes under consideration are discontinuous in time butconforming in space. Convergence of discrete schemes of arbitraryorder is proven. In addition, the convergence of discontinuousGalerkin approximations of the associated optimality system to thesolutions of the continuous optimality system is shown. The proofis based on stability estimates at arbitrary time points underminimal regularity assumptions, and a discrete compactnessargument for discontinuous Galerkin schemes (see Walkington[SINUM (June 2008) (submitted), preprint available at http://www.math.cmu.edu/~noelw], Sects. 3, 4).

Keywords

Discontinuous Galerkin approximationsdistributed controlsstability estimatessemi-linear parabolicPDE's.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 44 , Issue 1 , January 2010 , pp. 189 - 206
Copyright
© EDP Sciences, SMAI, 2009

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