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Volume 20, Issue 4
Full Discretisation of the Time Dependent Navier-Stokes Equations with Anisotropic Slip Boundary Condition

Rim Aldbaissy, Nancy Chalhoub, J. K. Djoko & Toni Sayah

DOI: 10.4208/ijnam2023-1021

Int. J. Numer. Anal. Mod., 20 (2023), pp. 497-517.

Published online: 2023-05

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  • 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.

  • Keywords

Power law slip boundary condition, Navier-Stokes equations, space-time discretization, monotonicity, error estimates.

  • AMS Subject Headings

65N30, 76M10, 35J85

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{IJNAM-20-497, author = {Aldbaissy , RimChalhoub , NancyDjoko , J. K. and Sayah , Toni}, title = {Full Discretisation of the Time Dependent Navier-Stokes Equations with Anisotropic Slip Boundary Condition}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2023}, volume = {20}, number = {4}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/10.4208/ijnam2023-1021}, url = {http://global-sci.org/intro/article_detail/ijnam/21713.html} }
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 -

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.

Aldbaissy , RimChalhoub , NancyDjoko , J. K. and Sayah , Toni. (2023). Full Discretisation of the Time Dependent Navier-Stokes Equations with Anisotropic Slip Boundary Condition. International Journal of Numerical Analysis and Modeling. 20 (4). 497-517. doi:10.4208/ijnam2023-1021
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