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

Authors:
Jorge San Martín;Loredana Smaranda;Takéo Takahashi
Affiliations:
Departamento de Ingeniería Matemática, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Casilla 170/3-Correo 3, Santiago, Chile and Centro de Modelamiento Mate ...;Centro de Modelamiento Matemático, Universidad de Chile, UMR 2071 CNRS-UChile, Casilla 170/3-Correo 3, Santiago, Chile and Department of Mathematics, Faculty of Mathematics and Computer Scien ...;Institut Elie Cartan Nancy, UMR 7502, INRIA-Nancy-Université-CNRS, BP 239, 54506 Vanduvre-lès-Nancy, Cedex, France and Team-Project CORIDA, INRIA Nancy Grand-Est, 615, rue du Jardin Bota ...
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

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Abstract

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 (ALE) 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.