TY  - JOUR
ID  - discovery10188004
UR  - https://doi.org/10.1051/m2an/2023106
N2  - In this article, we design and analyze an arbitrary-order stabilized finite element method to approximate the unique continuation problem for laminar steady flow described by the linearized incompressible Navier?Stokes equation. We derive quantitative local error estimates for the velocity, which account for noise level and polynomial degree, using the stability of the continuous problem in the form of a conditional stability estimate. Numerical examples illustrate the performances of the method with respect to the polynomial order and perturbations in the data. We observe that the higher order polynomials may be efficient for ill-posed problems, but are also more sensitive for problems with poor stability due to the ill-conditioning of the system.
Y1  - 2024/02/16/
PB  - EDP Sciences
A1  - Burman, Erik
A1  - Garg, Deepika
A1  - Preuss, Janosch
JF  - ESAIM: Mathematical Modelling and Numerical Analysis
SP  - 223
VL  - 58
EP  - 245
IS  - 1
AV  - public
SN  - 2822-7840
TI  - Data assimilation finite element method for the linearized Navier-Stokes equations with higher order polynomial approximation
KW  - Linearized Navier?Stokes? equations
KW  -  data assimilation
KW  -  stabilized finite element methods
KW  -  error estimates
N1  - © The authors. Published by EDP Sciences, SMAI 2024

Licence Creative CommonsThis is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
ER  -