TY - JOUR
T1 - Two-Grid Finite Element Methods for the Steady Navier-Stokes/Darcy Model
JO - East Asian Journal on Applied Mathematics
VL - 1
SP - 60
EP - 79
PY - 2018
DA - 2018/02
SN - 6
DO - http://doi.org/10.4208/eajam.080215.111215a
UR - https://global-sci.org/intro/article_detail/eajam/10773.html
KW - Navier-Stokes equations, Darcy’s law, multimodeling problems, two-grid method.
AB - <p style="text-align: justify;">Two-grid finite element methods for the steady Navier-Stokes/Darcy model
are considered. Stability and optimal error estimates in the $H^1$-norm for velocity and
piezometric approximations and the $L^2$-norm for pressure are established under mesh
sizes satisfying $h=H^2$. A modified decoupled and linearised two-grid algorithm is
developed, together with some associated optimal error estimates. Our method and
results extend and improve an earlier investigation, and some numerical computations
illustrate the efficiency and effectiveness of the new algorithm.</p>