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 - <p style="text-align: justify;">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.</p>