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.

中文翻译：

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低雷诺数线性化纳维-斯托克斯方程的数据同化有限元方法

在本文中，我们感兴趣的是设计和分析由线性化不可压缩 Navier-Stokes 方程描述的层流稳定流的有限元数据同化方法。我们提出了一种弱一致的稳定有限元方法，该方法从计算域子集中的速度测量重建整个流体流动。使用三球不等式形式的连续问题的稳定性，我们推导出速度的定量局部误差估计。数值模拟说明了这些收敛特性，我们最终将我们的方法应用于血管中的流动重建。