TY - JOUR
T1 - A Two-Grid Finite Element Method for Time-Dependent Incompressible Navier-Stokes Equations with Non-Smooth Initial Data
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 4
SP - 549
EP - 581
PY - 2015
DA - 2015/08
SN - 8
DO - http://doi.org/10.4208/nmtma.2015.m1414
UR - https://global-sci.org/intro/article_detail/nmtma/12423.html
KW - 
AB - <p style="text-align: justify;">We analyze here, a two-grid finite element method for the two dimensional time-dependent incompressible Navier-Stokes equations with non-smooth initial data. It involves solving the non-linear Navier-Stokes problem on a coarse grid of size $H$ and solving a Stokes problem on a fine grid of size $h, h &lt;&lt;H$. This method gives optimal convergence for velocity in $H^1$-norm and for pressure in $L^2$-norm. The analysis mainly focuses on the loss of regularity of the solution at $t = 0$ of the Navier-Stokes equations.</p>