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.
Domains
Numerical Analysis [math.NA]
Origin : Files produced by the author(s)
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