Full Discretisation of the Time Dependent Navier-Stokes Equations with Anisotropic Slip Boundary Condition
Year: 2023
Author: Rim Aldbaissy, Nancy Chalhoub, J. K. Djoko, Toni Sayah
International Journal of Numerical Analysis and Modeling, Vol. 20 (2023), Iss. 4 : pp. 497–517
Abstract
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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ijnam2023-1021
International Journal of Numerical Analysis and Modeling, Vol. 20 (2023), Iss. 4 : pp. 497–517
Published online: 2023-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 21
Keywords: Power law slip boundary condition Navier-Stokes equations space-time discretization monotonicity error estimates.