Full discretization of the time dependent Navier–Stokes equations with anisotropic slip boundary condition coupled with the convection-diffusion-reaction equation

Rim Aldbaissy ^[1] ; Nancy Chalhoub ^[1] ; Jules K. Djoko ^[2] ; Toni Sayah ^[3]
1. [1] Faculté des Ingénieurs, Université Saint-Joseph de Beyrouth
2. [2] School of Mathematical Sciences, University of North West, Pochefstroom
3. [3] Laboratoire de Mathématiques et Applications, Unité de recherche Mathématiques et Modélisation, Faculté des Sciences, Université Saint-Joseph de Beyrouth
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Localización: SeMA Journal: Boletín de la Sociedad Española de Matemática Aplicada, ISSN-e 2254-3902, ISSN 2254-3902, Vol. 82, Nº. 1, 2025, págs. 1-30
Idioma: inglés
DOI: 10.1007/s40324-024-00355-7
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Resumen
- 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.