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Creators/Authors contains: "Little, Samuel"

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  1. ; ; ; (, Communications in Nonlinear Science and Numerical Simulation)
    In this study, we conduct parameter estimation analysis on a data assimilation algorithm for two turbulence models: the simplified Bardina model and the Navier–Stokes-α model. Rigorous estimates are presented for the convergence of continuous data assimilation methods when the parameters of the turbulence models are not known a priori. Our approach involves creating an approximate solution for the turbulence models by employing an interpolant operator based on the observational data of the systems. The estimation depends on the parameter alpha in the models. Additionally, numerical simulations are presented to validate our theoretical results. 
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    Free, publicly-accessible full text available June 27, 2026
  2. ; ; ; (, Computational and applied mathematics)
    In this study, we perform a parameter error analysis of the 3D modified Leray-α model using both analytical and numerical approaches. First, we prove the global well-posedness and continuous dependence on the initial data for the assimilated system. Furthermore, under sufficient conditions on the physical parameters and norms of the true solution, we demon- strate that the true solution can be recovered from the approximate solution, with the error determined by the discrepancy between the true and approximate parameters. Numerical simulations are provided to validate the convergence criteria. 
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    Free, publicly-accessible full text available March 22, 2026