TY - JOUR
T1 - Full Discretisation of the Time Dependent Navier-Stokes Equations with Anisotropic Slip Boundary Condition
AU - Aldbaissy , Rim
AU - Chalhoub , Nancy
AU - Djoko , J. K.
AU - Sayah , Toni
JO - International Journal of Numerical Analysis and Modeling
VL - 4
SP - 497
EP - 517
PY - 2023
DA - 2023/05
SN - 20
DO - http://doi.org/10.4208/ijnam2023-1021
UR - https://global-sci.org/intro/article_detail/ijnam/21713.html
KW - Power law slip boundary condition, Navier-Stokes equations, space-time discretization, monotonicity, error estimates.
AB - <p style="text-align: justify;">In this work, we study theoretically and numerically the non-stationary Navier-Stokes’s equations under power law slip boundary condition. We establish existence of a unique
solution by using a semi-discretization in time combined with the weak convergence approach.
Next, we formulate and analyze the discretization in time and the finite element approximation
in space associated to the continuous problem. We derive optimal convergence in time and space
provided that the solution is regular enough on the slip zone. Iterative schemes for solving the
nonlinear problems is formulated and convergence is studied. Numerical experiments presented
confirm the theoretical findings.</p>