An a posteriori error analysis for dynamic viscoelastic problems
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 45 (2011) no. 5, p. 925-945

In this paper, a dynamic viscoelastic problem is numerically studied. The variational problem is written in terms of the velocity field and it leads to a parabolic linear variational equation. A fully discrete scheme is introduced by using the finite element method to approximate the spatial variable and an Euler scheme to discretize time derivatives. An a priori error estimates result is recalled, from which the linear convergence is derived under suitable regularity conditions. Then, an a posteriori error analysis is provided, extending some preliminary results obtained in the study of the heat equation and quasistatic viscoelastic problems. Upper and lower error bounds are obtained. Finally, some two-dimensional numerical simulations are presented to show the behavior of the error estimators.

DOI : https://doi.org/10.1051/m2an/2011002
Classification:  74H15,  65M15,  74D05,  74S05,  65M60
Keywords: viscoelasticity, dynamic problems, fully discrete approximations, a posteriori error estimates, finite elements, numerical simulations
@article{M2AN_2011__45_5_925_0,
     author = {Fern\'andez, J. R. and Santamarina, D.},
     title = {An a posteriori error analysis for dynamic viscoelastic problems},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {45},
     number = {5},
     year = {2011},
     pages = {925-945},
     doi = {10.1051/m2an/2011002},
     zbl = {1267.74052},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2011__45_5_925_0}
}
Fernández, J. R.; Santamarina, D. An a posteriori error analysis for dynamic viscoelastic problems. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 45 (2011) no. 5, pp. 925-945. doi : 10.1051/m2an/2011002. http://www.numdam.org/item/M2AN_2011__45_5_925_0/

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