TY - JOUR
T1 - Operator Splitting Methods for the Navier-Stokes Equations with Nonlinear Slip Boundary Conditions
JO - International Journal of Numerical Analysis and Modeling
VL - 4
SP - 785
EP - 805
PY - 2010
DA - 2010/07
SN - 7
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/752.html
KW - Navier-Stokes Equations, Nonlinear Slip Boundary Conditions, Operator Splitting Method, $\theta$-Scheme, Finite Element Approximation.
AB - <p style="text-align: justify;">In this paper, the $\theta$ scheme of operator splitting methods is applied
to the Navier-Stokes equations with nonlinear slip boundary conditions whose
variational formulation is the variational inequality of the second kind with
the Navier-Stokes operator. Firstly, we introduce the multiplier such that the
variational inequality is equivalent to the variational identity. Subsequently, we
give the $\theta$ scheme to compute the variational identity and consider the finite
element approximation of the $\theta$ scheme. The stability and convergence of the
$\theta$ scheme are showed. Finally, we give the numerical results.</p>