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We study continuous data assimilation (CDA) applied to projection and penaltymethods for the Navier-Stokes (NS) equations. Penalty and projection methodsare more efficient than consistent NS discretizations, however are lessaccurate due to modeling error (penalty) and splitting error (projection). Weshow analytically and numerically that with measurement data and properlychosen parameters, CDA can effectively remove these splitting and modelingerrors and provide long time optimally accurate solutions.

Removing splitting/modeling error in projection/penalty methods for Navier-Stokes simulations with continuous data assimilation