A problem with viscoelastic mixtures: numerical analysis and computational experiments. Issue 12 (10th September 2021)

• Record Type: Journal Article
• Authors: Fernández, J. R.; Masid, M.; Magaña, A.; Quintanilla, R.
• Is Part Of: Applicable analysis. Volume 100:Issue 12(2021)
• Page Start: 2684
• Page End: 2705
• Publication Date: 2021-09-10
• Subjects: Mixtures -- viscoelasticity -- finite element approximations -- error estimates -- numerical simulations; 74E30 -- 74D05 -- 65M60 -- 65M15 -- 65M12; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2019.1698721
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: 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.