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Optimal control of the convection-diffusion equation using stabilized finite element methods

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Abstract

In this paper we analyze the discretization of optimal control problems governed by convection-diffusion equations which are subject to pointwise control constraints. We present a stabilization scheme which leads to improved approximate solutions even on corse meshes in the convection dominated case. Moreover, the in general different approaches “optimize-then- discretize” and “discretize-then-optimize” coincide for the proposed discretization scheme. This allows for a symmetric optimality system at the discrete level and optimal order of convergence.

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Correspondence to Boris Vexler.

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Becker, R., Vexler, B. Optimal control of the convection-diffusion equation using stabilized finite element methods. Numer. Math. 106, 349–367 (2007). https://doi.org/10.1007/s00211-007-0067-0

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