@article{Bazarra2022, 
author = {Noelia Bazarra and José R. Fernández and Ramón Quintanilla},
title = {On the mixtures of MGT viscoelastic solids},
year = {2022},
journal = {Electronic Research Archive},
volume = {30},
number = {12},
pages = {4318-4340},
keywords = {viscoelasticity, existence and uniqueness, finite elements, energy decay, mixtures, linear semigroups},
url = {https://www.sciopen.com/article/10.3934/era.2022219},
doi = {10.3934/era.2022219},
abstract = {In this paper, we study, from both analytical and numerical points of view, a problem involving a mixture of two viscoelastic solids. An existence and uniqueness result is proved using the theory of linear semigroups. Exponential decay is shown for the one-dimensional case. Then, fully discrete approximations are introduced using the finite element method and the implicit Euler scheme. Some a priori error estimates are obtained and the linear convergence is derived under suitable regularity conditions. Finally, one- and two-dimensional numerical simulations are presented to demonstrate the convergence, the discrete energy decay and the behavior of the solution.}
}