Abstract
In this article, we consider the time dependent convection–diffusion–reaction equation coupled with the Navier–Stokes system subject partially to anisotropic slip boundary condition. We formulate the weak problem, and construct the weak solutions by using the approximation approach combined with some compactness results. The discrete solution is constructed by using the finite element method in space and the implicit Euler scheme in time. The convergence of the discrete solution is examined thanks to a priori errors estimation, and the rate of convergence is obtained. We propose an iterative scheme and investigate its convergence using the weak convergence approach. Finally, numerical investigations are performed to validate the theoretical results presented.
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Aldbaissy, R., Chalhoub, N., Djoko, J.K. et al. Full discretization of the time dependent Navier–Stokes equations with anisotropic slip boundary condition coupled with the convection–diffusion–reaction equation. SeMA (2024). https://doi.org/10.1007/s40324-024-00355-7
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DOI: https://doi.org/10.1007/s40324-024-00355-7
Keywords
- Power law slip boundary condition
- Time dependent Navier–Stokes equations
- Heat equation
- Space–time discretization
- Error estimates