Data assimilation finite element method for the linearized Navier-Stokes equations in the low Reynolds regime

Muriel Boulakia (1, 2) , Erik Burman (3) , Miguel Angel Fernández (2) , Colette Voisembert (2)

1 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions
2 COMMEDIA - COmputational Mathematics for bio-MEDIcal Applications
3 UCL London - Department of Mathematics

In this paper we are interested in designing and analyzing a finite element data assimilation method for laminar steady flow described by the linearized incompressible Navier-Stokes equation. We propose a weakly consistent stabilized finite element method which reconstructs the whole fluid flow from velocity measurements in a subset of the computational domain. Using the stability of the continuous problem in the form of a three balls inequality, we derive quantitative local error estimates for the velocity. Numerical simulations illustrate these convergences properties and we finally apply our method to the flow reconstruction in a blood vessel.

Mots clés: 10.1088/1361-6420/ab9161

Domaines: Analyse numérique [math.NA]

Muriel Boulakia, Erik Burman, Miguel Angel Fernández, Colette Voisembert. Data assimilation finite element method for the linearized Navier-Stokes equations in the low Reynolds regime. Inverse Problems, 2020, 36, pp.085003. ⟨10.1088/1361-6420/ab9161⟩. ⟨hal-02318504⟩