TY - JOUR
T1 - Error Estimates for the Second Order Semi-Discrete Stabilized Gauge-Uzawa Method for the Navier-Stokes Equations
AU - J.-H. Pyo
JO - International Journal of Numerical Analysis and Modeling
VL - 1
SP - 24
EP - 41
PY - 2013
DA - 2013/10
SN - 10
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/557.html
KW - Projection method, Gauge-Uzawa method, the rotational form of pressure correction method, Navier-Stokes equations, incompressible fluids.
AB - <p style="text-align: justify;">The Gauge-Uzawa method [GUM], which is a projection type algorithm
to solve the time depend Navier-Stokes equations, has been constructed in [14] and
enhanced in [15, 17] to apply to more complicated problems. Even though GUM possesses many advantages theoretically and numerically, the studies on GUM have been
limited on the first order backward Euler scheme except normal mode error estimate
in [16]. The goal of this paper is to research the 2nd order GUM. Because the classical
2nd order GUM which is studied in [16] needs rather strong stability condition, we
modify GUM to be unconditionally stable method using BDF2 time marching. The
stabilized GUM is equivalent to the rotational form of pressure correction method and
the errors are already estimated in [8] for the Stokes equations. In this paper, we will
evaluate errors of the stabilized GUM for the Navier-Stokes equations. We also prove
that the stabilized GUM is an unconditionally stable method for the Navier-Stokes
equations. So we conclude that the rotational form of pressure correction method in
[8] is also unconditionally stable scheme and that the accuracy results in [8] are valid
for the Navier-Stokes equations.</p>