An a posteriori error analysis for dynamic viscoelastic problems

J. R. Fernández; D. Santamarina

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2011)

  • Volume: 45, Issue: 5, page 925-945
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Fernández, J. R., and Santamarina, D.. "An a posteriori error analysis for dynamic viscoelastic problems." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 45.5 (2011): 925-945. <http://eudml.org/doc/273316>.

@article{Fernández2011,
abstract = {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.},
author = {Fernández, J. R., Santamarina, D.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {viscoelasticity; dynamic problems; fully discrete approximations; a posteriori error estimates; finite elements; numerical simulations},
language = {eng},
number = {5},
pages = {925-945},
publisher = {EDP-Sciences},
title = {An a posteriori error analysis for dynamic viscoelastic problems},
url = {http://eudml.org/doc/273316},
volume = {45},
year = {2011},
}

TY - JOUR
AU - Fernández, J. R.
AU - Santamarina, D.
TI - An a posteriori error analysis for dynamic viscoelastic problems
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2011
PB - EDP-Sciences
VL - 45
IS - 5
SP - 925
EP - 945
AB - 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.
LA - eng
KW - viscoelasticity; dynamic problems; fully discrete approximations; a posteriori error estimates; finite elements; numerical simulations
UR - http://eudml.org/doc/273316
ER -

References

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