TY - JOUR
T1 - Removing Splitting/Modeling Error in Projection/Penalty Methods for Navier-Stokes Simulations with Continuous Data Assimilation
AU - Hawkins , Elizabeth
AU - Rebholz , Leo G.
AU - Vargun , Duygu
JO - Communications in Mathematical Research 
VL - 1
SP - 1
EP - 29
PY - 2023
DA - 2023/12
SN - 40
DO - http://doi.org/10.4208/cmr.2023-0008
UR - https://global-sci.org/intro/article_detail/cmr/22279.html
KW - Navier-Stokes equations, projection method, penalty method, continuous
data assimilation.
AB - <p style="text-align: justify;">We study continuous data assimilation (CDA) applied to projection
and penalty methods for the Navier-Stokes (NS) equations. Penalty and projection methods are more efficient than consistent NS discretizations, however
are less accurate due to modeling error (penalty) and splitting error (projection). We show analytically and numerically that with measurement data and
properly chosen parameters, CDA can effectively remove these splitting and
modeling errors and provide long time optimally accurate solutions.</p>