Stability and convergence of an hybrid finite volume-finite element method for a multiphasic incompressible fluid model

Caterina Calgaro (1) , Meriem Ezzoug (2) , Ezzeddine Zahrouni (3, 2)

1 RAPSODI - Reliable numerical approximations of dissipative systems
2 Département de Mathématiques [Monastir]
3 UCAR - Université de Carthage (Tunisie)

In this paper, we construct a fully discrete numerical scheme for approximating a two-dimensional multiphasic incompressible fluid model, also called the Kazhikhov-Smagulov model. We use a first-order time discretization and a splitting in time to allow us the construction of an hybrid scheme which combines a Finite Volume and a Finite Element method. Consequently, at each time step, one only needs to solve two decoupled problems, the first one for the density and the second one for the velocity and pressure. We will prove the stability of the scheme and the convergence towards the global in time weak solution of the model.

Mots clés: convergence; stability; Finite Volume method; Finite Element method; Kazhikhov-Smagulov model

Domaines: Analyse numérique [math.NA]

Caterina Calgaro, Meriem Ezzoug, Ezzeddine Zahrouni. Stability and convergence of an hybrid finite volume-finite element method for a multiphasic incompressible fluid model. Communications on Pure and Applied Analysis, 2018, 17 (2), pp.429-448. ⟨10.3934/cpaa.2018024⟩. ⟨hal-01586201⟩