Universitat Politècnica de Catalunya. Departament de Matemàtiques, Universitat Politècnica de Catalunya. GRTJ - Grup de Recerca en Teoria de Jocs, Universitat Politècnica de Catalunya. GRAA - Grup de Recerca en Anàlisi Aplicada
Source:
UPCommons. Portal del coneixement obert de la UPC Universitat Politècnica de Catalunya (UPC) Recercat. Dipósit de la Recerca de Catalunya instname
In this paper, we study, from the numerical point of view, a dynamic problem involving a mixture of two viscoelastic solids. The mechanical problem is written as a system of two coupled partial differential equations. Its variational formulation is derived and an existence and uniqueness result, and an energy decay property, are recalled. Then, fully discrete approximations are introduced by using the classical finite element method and the implicit Euler scheme. A discrete stability property and a priori error estimates are shown, from which we deduce the linear convergence of the algorithm. Finally, some numerical simulations, including examples in one and two dimensions, are presented to show the accuracy of the approximation and the behaviour of the solution.