TY - JOUR
T1 - Two-level Penalty Finite Element Methods for Navier-Stokes Equations with Nonlinear Slip Boundary Conditions
AU - R. An & Y. Li
JO - International Journal of Numerical Analysis and Modeling
VL - 3
SP - 608
EP - 623
PY - 2014
DA - 2014/11
SN - 11
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/544.html
KW - Navier-Stokes Equations
KW - Nonlinear Slip Boundary Conditions
KW - Variational Inequality Problem
KW - Penalty Finite Element Method
KW - Two-Level Methods
AB - The two-level penalty finite element methods for Navier-Stokes equations with non-linear slip boundary conditions are investigated in this paper, whose variational formulation is
the Navier-Stokes type variational inequality problem of the second kind. The basic idea is to
solve the Navier-Stokes type variational inequality problem on a coarse mesh with mesh size H in
combining with solving a Stokes type variational inequality problem for simple iteration or solving
a Oseen type variational inequality problem for Oseen iteration on a fine mesh with mesh size h.
The error estimate obtained in this paper shows that if H = O(h^{5/9}), then the two-level penalty
methods have the same convergence orders as the usual one-level penalty finite element method,
which is only solving a large Navier-Stokes type variational inequality problem on the fine mesh.
Hence, our methods can save a amount of computational work.