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.

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

Paper coordinates

E. Burman, M. Nechita, L. Oksanen, A stabilized finite element method for inverse problems subject to the convection-diffusion equation. II: convection-dominated regime, Numer. Math., 150:769-801, 2022, DOI: https://doi.org/10.1007/s00211-022-01268-1

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About this paper

Journal

Numerische Mathematik

Publisher Name

Springer

Print ISSN

0029-599X

Online ISSN

0945-3245

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