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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.
Keywords :
10.1088/1361-6420/ab9161
Cited literature [36 references]
https://hal.inria.fr/hal-02318504
Contributor : Miguel Angel Fernández <>
Submitted on : Thursday, October 17, 2019 - 10:32:12 AM
Last modification on : Wednesday, June 2, 2021 - 4:26:50 PM
Long-term archiving on: : Saturday, January 18, 2020 - 1:29:34 PM
Contributor : Miguel Angel Fernández <>
Submitted on : Thursday, October 17, 2019 - 10:32:12 AM
Last modification on : Wednesday, June 2, 2021 - 4:26:50 PM
Long-term archiving on: : Saturday, January 18, 2020 - 1:29:34 PM
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