## 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.

## Authors

**Erik Burman**

Department of Mathematics, University College London, Gower Street, London UK, WC1E 6BT

**Mihai Nechita**

Department of Mathematics, University College London, Gower Street, London UK, WC1E 6BT

**Lauri Oksanen**

Department of Mathematics, University College London, Gower Street, London UK, WC1E 6BT

## Keywords

convection-diffusion equation, convection-dominated, unique continuation, ill-posed problem

To appear in Numerische Mathematik. Preprint available at https://arxiv.org/pdf/2006.13201.pdf

##### Cite this paper as:

E. Burma, M. Nechita, L. Oksanen, *A stabilized finite element method for inverse problems subject to the convection-diffusion equation. II: convection-dominated regime, Numer. Math. (to appear)*

## Notes

The paper was accepted in Numerische Mathematik, we are now waiting for proofreading. The confirmation of acceptance from the editor is here.

## About this paper

##### Journal

Numerische Mathematik

##### Publisher Name

Springer

##### DOI

Not available yet.

##### Print ISSN

0029-599X

##### Online ISSN

0945-3245

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