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Volume 40, Issue 3
Numerical Analysis of a Problem Involving a Viscoelastic Body with Double Porosity

Noelia Bazarra, José R. Fernández, Mari Carme Leseduarte, Antonio Magaña & Ramón Quintanilla

DOI: 10.4208/jcm.2010-m2020-0043

J. Comp. Math., 40 (2022), pp. 415-436.

Published online: 2022-02

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  • 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.

  • Keywords

Viscoelasticity with double porosity, Finite elements, A priori estimates, Numerical simulations.

  • AMS Subject Headings

65M60, 37N15, 74F05, 65M12

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

noabaza@hotmail.com (Noelia Bazarra)

jose.fernandez@uvigo.es (José R. Fernández)

Mari.Carme.Leseduarte@upc.edu (Mari Carme Leseduarte)

antonio.magana@upc.edu (Antonio Magaña)

Ramon.Quintanilla@upc.edu (Ramón Quintanilla)

  • BibTex
  • RIS
  • TXT
@Article{JCM-40-415, author = {Bazarra , NoeliaFernández , José R.Leseduarte , Mari CarmeMagaña , Antonio and Quintanilla , Ramón}, title = {Numerical Analysis of a Problem Involving a Viscoelastic Body with Double Porosity}, journal = {Journal of Computational Mathematics}, year = {2022}, volume = {40}, number = {3}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2010-m2020-0043}, url = {http://global-sci.org/intro/article_detail/jcm/20244.html} }
TY - JOUR T1 - Numerical Analysis of a Problem Involving a Viscoelastic Body with Double Porosity AU - Bazarra , Noelia AU - Fernández , José R. AU - Leseduarte , Mari Carme AU - Magaña , Antonio AU - Quintanilla , Ramón JO - Journal of Computational Mathematics VL - 3 SP - 415 EP - 436 PY - 2022 DA - 2022/02 SN - 40 DO - http://doi.org/10.4208/jcm.2010-m2020-0043 UR - https://global-sci.org/intro/article_detail/jcm/20244.html KW - Viscoelasticity with double porosity, Finite elements, A priori estimates, Numerical simulations. AB -

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.

Bazarra , NoeliaFernández , José R.Leseduarte , Mari CarmeMagaña , Antonio and Quintanilla , Ramón. (2022). Numerical Analysis of a Problem Involving a Viscoelastic Body with Double Porosity. Journal of Computational Mathematics. 40 (3). 415-436. doi:10.4208/jcm.2010-m2020-0043
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