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    Continuous data assimilation of a discretized barotropic vorticity model of geophysical flow
    (Pergamon-Elsevier Science Ltd, 2024) Akbas, Mine; Diegel, Amanda E.; Rebholz, Leo G.
    We consider continuous data assimilation applied to a finite element spatial discretization and backward difference temporal discretization of the barotropic vorticity model of geophysical flow. We prove that with sufficient measurement data and properly chosen nudging parameter (guided by our analysis), the proposed algorithm achieves optimal long-time accuracy for any initial condition. While our analysis requires nudging of both the streamfunction and vorticity, our numerical tests indicate that nudging only the streamfunction can be sufficient.
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    FINITE ELEMENT ANALYSIS OF LINEARLY EXTRAPOLATED BLENDED BACKWARD DIFFERENCE FORMULA (BLEBDF) FOR THE NATURAL CONVECTION FLOWS
    (Hüseyin ÇAKALLI, 2024) Ak, Merve; Akbas, Mine
    In this paper, we study the stability and convergence of fully discrete finite element method with grad-div stabilization for the incompressible non-isothermal fluid flows. The proposed scheme uses finite element discretization in space and linearly extrapolated blended Backward Differentiation Formula (BLEBDF) in time. We prove the unconditional stability over finite time interval and optimally convergence of the scheme. We also present numerical experiments to verify our theoretical convergence rates and show the reliability of the scheme.