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

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.

keywords: Kazhikhov-Smagulov model finite volume method finite element method stability convergence

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