Fading regularization method for the stationary Stokes data assimilation problem
Abstract
In this study, we address the ill-posed stationary Stokes data assimilation (DA) problem using the fading regularization method (FRM). It involves reconstructing the fluid velocity field throughout the study domain Ω in R n , where n is the dimension of the space, as well as the boundary conditions, using knowledge of some observations of the fluid velocity field u o b s measured within a limited domain ω included in Ω . Using the FRM, the main ill-posed problem is transformed into a sequence of well-posed constraint optimization problems and simplifies the resolution of DA problem. Additionally, we prove the convergence of both the continuous and the discrete formulations. This method is implemented numerically using the method of fundamental solutions (MFS) and several numerical simulations are shown to illustrate the performance of the algorithm in terms of efficiency, accuracy, convergence, stability, and robustness to noisy data, as well as its ability to deblur the data in ω .
Related
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BibTeX
@article{zayeni2026fading,
title = {{Fading regularization method for the stationary Stokes data assimilation problem}},
author = {Hatem Zayeni and Amel Ben Abda and Franck Delvare},
journal = {Computer Methods in Applied Mechanics and Engineering},
year = {2026},
month = sep,
doi = {10.1016/j.cma.2024.117450},
url = {https://hal.science/hal-05740730v1},
note = {CC BY-NC},
}
RIS
TY - JOUR
TI - Fading regularization method for the stationary Stokes data assimilation problem
AU - Hatem Zayeni
AU - Amel Ben Abda
AU - Franck Delvare
PY - 2026
DA - 2026/09/07
JO - Computer Methods in Applied Mechanics and Engineering
DO - 10.1016/j.cma.2024.117450
UR - https://hal.science/hal-05740730v1
AB - In this study, we address the ill-posed stationary Stokes data assimilation (DA) problem using the fading regularization method (FRM). It involves reconstructing the fluid velocity field throughout the study domain Ω in R n , where n is the dimension of the space, as well as the boundary conditions, using knowledge of some observations of the fluid velocity field u o b s measured within a limited domain ω included in Ω . Using the FRM, the main ill-posed problem is transformed into a sequence of well-posed constraint optimization problems and simplifies the resolution of DA problem. Additionally, we prove the convergence of both the continuous and the discrete formulations. This method is implemented numerically using the method of fundamental solutions (MFS) and several numerical simulations are shown to illustrate the performance of the algorithm in terms of efficiency, accuracy, convergence, stability, and robustness to noisy data, as well as its ability to deblur the data in ω .
SN - 0045-7825
SN - 1879-2138
ER -