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Zbl 1191.65074
Chrysafinos, Konstantinos
Convergence of discontinuous Galerkin approximations of an optimal control problem associated to semilinear parabolic PDE's. (English)
[J] ESAIM, Math. Model. Numer. Anal. 44, No. 1, 189-206 (2010). ISSN 0764-583X; ISSN 1290-3841/e

Author's abstract: The author considers optimal control problems associated to the minimization of the tracking functional $$J(y,g)= \tfrac12 \int^T_0\|y-U\|^2_{L^2(\Omega)}\,dt+\tfrac\alpha2\int^T_0\|g\|^2_{L^2(\Omega)}\, dt$$ subject to the constraints $$\align y_t-\text{div}[A(x)\nabla y] +\phi(y) = f + g \quad & \text{in }(0,T)\times \Omega,\\ y=0\quad & \text{on }(0,T)\times \Gamma,\\ y(0,x)=y_0\quad & \text{in }\Omega.\endalign$$ For these problems, a discontinuous Galerkin finite element method is examined and the convergence is proven.
[Hans Benker (Merseburg)]

MSC 2000:: *65K10 Optimization techniques (numerical methods)
65M60 Finite numerical methods (IVP of PDE)
49J20 Optimal control problems with PDE (existence)
49M25 Finite difference methods

Keywords: distributed controls; stability estimates; semi-linear parabolic PDE's; optimal control; discontinuous Galerkin finite element method; convergence

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