Numerical analysis of data assimilation for slightly compressible flow
Abstract
Continuous data assimilation improves flow predictions by continually nudging a model toward available observational data. For slightly compressible flow, a recent model addresses the limitations of velocity-only nudging by assimilating both velocity and pressure data and nudging both quantities into the incompressible Navier-Stokes equations [5]; continuous-in-time error estimates and preliminary experiments show that this joint nudging is effective and substantially reduces the model error relative to velocity-only nudging. Motivated by these results, we carry out the numerical analysis of the model and its finite element discretizations. We establish stability and error estimates for the semi-discrete scheme and for the fully discrete, linearized backward Euler scheme. The analysis shows an infinite predictability horizon: the effect of the initial error decays exponentially in time, and the model error is first order in the observation resolution H and of order μ1−1/2 in the pressure nudging parameter μ1. Balancing these two error terms, we choose μ1=𝒪(H−2), which yields the optimal convergence rate. Numerical experiments confirm the predicted rates.
Related
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BibTeX
@misc{cıbık2026numerical,
title = {{Numerical analysis of data assimilation for slightly compressible flow}},
author = {Aytekin Çıbık and Rui Fang},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.27647},
eprint = {2608.27647},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.27647},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Numerical analysis of data assimilation for slightly compressible flow
AU - Aytekin Çıbık
AU - Rui Fang
PY - 2026
DA - 2026/08/27
PB - arXiv
DO - 10.48550/arxiv.2608.27647
UR - https://arxiv.org/abs/2608.27647
AB - Continuous data assimilation improves flow predictions by continually nudging a model toward available observational data. For slightly compressible flow, a recent model addresses the limitations of velocity-only nudging by assimilating both velocity and pressure data and nudging both quantities into the incompressible Navier-Stokes equations [5]; continuous-in-time error estimates and preliminary experiments show that this joint nudging is effective and substantially reduces the model error relative to velocity-only nudging. Motivated by these results, we carry out the numerical analysis of the model and its finite element discretizations. We establish stability and error estimates for the semi-discrete scheme and for the fully discrete, linearized backward Euler scheme. The analysis shows an infinite predictability horizon: the effect of the initial error decays exponentially in time, and the model error is first order in the observation resolution H and of order μ_1^−1/2 in the pressure nudging parameter μ_1. Balancing these two error terms, we choose μ_1=𝒪(H^−2), which yields the optimal convergence rate. Numerical experiments confirm the predicted rates.
ER -