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- W4213035957 abstract "We consider the numerical approximation of the ill-posed data assimilation problem for stationary convection-diffusion equations and extend our previous analysis in [Numer. Math. 144, 451--477, 2020] to the convection-dominated regime. Slightly adjusting the stabilized finite element method proposed for dominant diffusion, we draw upon a local error analysis to obtain quasi-optimal convergence along the characteristics of the convective field through the data set. The weight function multiplying the discrete solution is taken to be Lipschitz and a corresponding super approximation result (discrete commutator property) is proven. The effect of data perturbations is included in the analysis and we conclude the paper with some numerical experiments." @default.
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- W4213035957 date "2022-02-18" @default.
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- W4213035957 title "A stabilized finite element method for inverse problems subject to the convection–diffusion equation. II: convection-dominated regime" @default.
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- W4213035957 doi "https://doi.org/10.1007/s00211-022-01268-1" @default.
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