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arXiv · 2006.13201

A stabilized finite element method for inverse problems subject to the convection-diffusion equation. II: convection-dominated regime

Erik Burman·Mihai Nechita·Lauri Oksanen
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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.

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Erik Burman, Mihai Nechita, Lauri Oksanen. 2020-06-23. A stabilized finite element method for inverse problems subject to the convection-diffusion equation. II: convection-dominated regime. https://doi.org/10.1007/s00211-022-01268-1

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