Numerical Analysis of a Problem Involving a Viscoelastic Body with Double Porosity

Numerical Analysis of a Problem Involving a Viscoelastic Body with Double Porosity

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.

Author Details

Noelia Bazarra

José R. Fernández

Mari Carme Leseduarte

Antonio Magaña

Ramón Quintanilla