Boundary control of parabolic systems: Finite-element approximation

Finite-element approximation of a Dirichlet type boundary control problem for parabolic systems is considered. An approach based on the direct approximation of an input-output semigroup formula is applied. Error estimates inL2[OT; L2(Ω)] andL2[OT; L2(Γ)] norms are derived for optimal state and optimal control, respectively. It turns out that these estimates areoptimal with respect to the approximation theoretic properties.

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