Continuous data assimilation applied to a velocity-vorticity formulation of the 2D Navier-Stokes equations

<p style='text-indent:20px;'>We study a continuous data assimilation (CDA) algorithm for velocity-vorticity formulation of the 2D Navier-Stokes equations in two cases: nudging applied to velocity and vorticity, only. We prove that under typical finite element spatial discretization backward Euler temporal discretization, application CDA preserves unconditional long-time stability property method provides optimal accuracy. These properties hold if is only velocity, also vorticity then accuracy achieved more rapidly time. Numerical tests illustrate theory, show its effectiveness on an problem channel flow past flat plate.</p>