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

Abstract : 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.
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Submitted on : Thursday, October 17, 2019 - 10:32:12 AM
Last modification on : Monday, October 21, 2019 - 10:07:07 AM

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  • HAL Id : hal-02318504, version 1

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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. 2019. ⟨hal-02318504⟩

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