no. 1
Convergence of discontinuous Galerkin approximations of an optimal control problem associated to semilinear parabolic PDE's
ESAIM: Modélisation mathématique et analyse numérique, Tome 44 (2010) no. 1, pp. 189-206.

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).

DOI : 10.1051/m2an/2009046
Classification : 65M60, 49J20
Mots clés : discontinuous Galerkin approximations, distributed controls, stability estimates, semi-linear parabolic PDE's 
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     title = {Convergence of discontinuous {Galerkin} approximations of an optimal control problem associated to semilinear parabolic {PDE's}},
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Chrysafinos, Konstantinos. Convergence of discontinuous Galerkin approximations of an optimal control problem associated to semilinear parabolic PDE's. ESAIM: Modélisation mathématique et analyse numérique, Tome 44 (2010) no. 1, pp. 189-206. doi : 10.1051/m2an/2009046. http://archive.numdam.org/articles/10.1051/m2an/2009046/

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