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Equivalent a posteriori error estimates for elliptic optimal control problems with \(L^1\)-control cost. (English) Zbl 1442.49036

Summary: An elliptic optimal control problem involving the \(L^1\) norm of the control in the cost functional is considered in this paper. We use the full discretization and the variational discretization to approximate the control problem and the efficient and reliable a posteriori error estimates are obtained for the two cases. For the variational discretization, we also analyze the convergence of adaptive finite element methods. In the end, some examples are provided to validate our analysis.

MSC:

49M25 Discrete approximations in optimal control
65N15 Error bounds for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
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