Year: 2022
Author: Noelia Bazarra, José R. Fernández, Mari Carme Leseduarte, Antonio Magaña, Ramón Quintanilla
Journal of Computational Mathematics, Vol. 40 (2022), Iss. 3 : pp. 415–436
Abstract
We study from a numerical point of view a multidimensional problem involving a viscoelastic body with two porous structures. The mechanical problem leads to a linear system of three coupled hyperbolic partial differential equations. Its corresponding variational formulation gives rise to three coupled parabolic linear equations. An existence and uniqueness result, and an energy decay property, are recalled. Then, fully discrete approximations are introduced using the finite element method and the implicit Euler scheme. A discrete stability property and a priori error estimates are proved, from which the linear convergence of the algorithm is derived under suitable additional regularity conditions. Finally, some numerical simulations are performed in one and two dimensions to show the accuracy of the approximation and the behaviour of the solution.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2010-m2020-0043
Journal of Computational Mathematics, Vol. 40 (2022), Iss. 3 : pp. 415–436
Published online: 2022-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Viscoelasticity with double porosity Finite elements A priori estimates Numerical simulations.