Abstract
We present a method for the numerical approximation of distributed optimal control problems constrained by parabolic partial differential equations. We complement the first-order optimality condition by a recently developed space-time variational formulation of parabolic equations which is coercive in the energy norm, and a Lagrange multiplier. Our final formulation fulfills the Babuška–Brezzi conditions on the continuous as well as discrete level, without restrictions. Consequently, we can allow for final-time desired states, and obtain an a posteriori error estimator which is efficient and reliable up to an additional discretization error of the adjoint problem. Numerical experiments confirm our theoretical findings.
Funding source: Comisión Nacional de Investigación Científica y Tecnológica
Award Identifier / Grant number: 1210579
Award Identifier / Grant number: 1210391
Funding statement: Supported by Conicyt Chile through projects FONDECYT 1210579 (M. Karkulik) and 1210391 (T. Führer).
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