Convergence of a finite element/ALE method for the Stokes equations in a domain depending on time

Jorge San Martin (1, 2) , Loredana Smaranda (1, 2) , Takéo Takahashi (3, 4)

1 DIM - Departamento de Ingeniería Matemática [Santiago]
2 CMM - Centre de modélisation mathématique / Centro de Modelamiento Matemático [Santiago]
3 IECN - Institut Élie Cartan de Nancy
4 CORIDA - Robust control of infinite dimensional systems and applications

We consider the approximation of the unsteady Stokes equations in a time dependent domain when the motion of the domain is given. More precisely, we apply the finite element method to an Arbitrary Lagrangian Eulerian (A.L.E.) formulation of the system. Our main results state the convergence of the solutions of the semi-discretized (with respect to the space variable) and of the fully-discrete problems towards the solutions of the Stokes system.

Domaines: Analyse numérique [math.NA]

Jorge San Martin, Loredana Smaranda, Takéo Takahashi. Convergence of a finite element/ALE method for the Stokes equations in a domain depending on time. Journal of Computational and Applied Mathematics, 2009, 230 (2), pp.521-545. ⟨10.1016/j.cam.2008.12.021⟩. ⟨hal-00275223⟩