Data assimilation finite element method for the linearized Navier–Stokes equations in the low Reynolds regime. (20th August 2020)

• Record Type: Journal Article
• Authors: Boulakia, Muriel; Burman, Erik; Fernández, Miguel A.; Voisembert, Colette
• Is Part Of: Inverse problems. Volume 36:Number 8(2020)
• Publication Date: 2020-08-20
• Subjects: linearized Navier–Stokes' equations -- data assimilation -- stabilized finite element methods -- three balls inequality -- error estimates; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/ab9161
• Languages: English
• ISSNs: 0266-5611

Abstract

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 noisy 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 convergence properties and we finally apply our method to the flow reconstruction in a blood vessel.