arXiv subjects

Débora A. F. Albanez

Publications and source records attributed to Débora A. F. Albanez.

4 recordsLinked to original sources

arXiv2025

Recovering the Parameter $α$ in the Simplified Bardina Model through Continuous Data Assimilation

In this study, we develop a continuous data assimilation algorithm to recover the parameter $α$ in the simplified Bardina model. Our method utilizes the observations of finitely many Fourier modes by using a nudging framework that involves recursive parameter updates. We provide a rigorous convergence analysis, showing that the approximate parameter approaches the true value under suitable conditions, while the approximate solution also converges to the true solution.

math.DS↗

arXiv2024

Parameter Error Analysis for the 3D Modified Leray-alpha Model: Analytical and Numerical Approaches

In this study, we conduct a parameter error analysis for the 3D modified Leray-$α$ model using both analytical and numerical approaches. We first prove the global well-posedness and continuous dependence of initial data for the assimilated system. Furthermore, given sufficient conditions on the physical parameters and norms of the true solution, we demonstrate that the true solution can be recovered from the approximation solution, with an error determined by the discrepancy between the true and approximating parameters. Numerical simulations are provided to validate the convergence criteria.

math.NA↗

arXiv2022

Parameter analysis in continuous data assimilation for three-dimensional Brinkman-Forchheimer-extended Darcy

In this paper, we study analytically the long-time behavior of three-dimensional Brinkman-Forchheimer-extended Darcy model, in the context that the parameters related to the damping nonlinear term are unknown. This work is inspired by the approach firstly introduced for two-dimensional Navier-Stokes equations by Carlson, Hudson and Larios. We show estimates in L2 and H1 for large-time error between the true solution and the assimilated solution, which is constructed with the unknown damping parameters and observational measurements obtained continuously in time from a continuous data assimilation technique proposed by Azouani, Olson and Titi.

math.AP↗

arXiv2014

Continuous data assimilation for the three-dimensional Navier-Stokes-$α$

Motivated by the presence of a finite number of determining parameters (degrees of freedom) such as modes, nodes and local spatial averages for dissipative dynamical systems, we present a continuous data assimilation algorithm for the three-dimensional Navier-Stokes-$α$ model. This algorithm consists of introducing a nudging process through general type of approximation interpolation operator (that is constructed from observational measurements) that synchronizes the large spatial scales of the approximate solutions with those of the unknown solutions the Navier-Stokes-$α$ equations that corresponds to these measurements. Our main result provides conditions on the finite-dimensional spatial resolution of the collected data, sufficient to guarantee that the approximating solution, that is obtained from these collected data, converges to the unkown reference solution (physical reality) over time. These conditions are given in terms of some physical parameters, such as kinematic viscosity, the size of the domain and the forcing term.

math.AP↗