A stabilized finite element method for inverse problems subject to the convection-diffusion equation. II: convection-dominated regime
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.
Keywords
Cite
@article{arxiv.2006.13201,
title = {A stabilized finite element method for inverse problems subject to the convection-diffusion equation. II: convection-dominated regime},
author = {Erik Burman and Mihai Nechita and Lauri Oksanen},
journal= {arXiv preprint arXiv:2006.13201},
year = {2022}
}
Comments
25 pages, 16 figures; final published version