# An a posteriori error analysis for dynamic viscoelastic problems

J. R. Fernández; D. Santamarina

ESAIM: Mathematical Modelling and Numerical Analysis (2011)

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

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topFernández, J. R., and Santamarina, D.. "An a posteriori error analysis for dynamic viscoelastic problems." ESAIM: Mathematical Modelling and Numerical Analysis 45.5 (2011): 925-945. <http://eudml.org/doc/197536>.

@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},

keywords = {Viscoelasticity; dynamic problems; fully discrete approximations; a posteriori error estimates; finite elements; numerical simulations; viscoelasticity; a posteriori error estimates},

language = {eng},

month = {4},

number = {5},

pages = {925-945},

publisher = {EDP Sciences},

title = {An a posteriori error analysis for dynamic viscoelastic problems},

url = {http://eudml.org/doc/197536},

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

DA - 2011/4//

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; viscoelasticity; a posteriori error estimates

UR - http://eudml.org/doc/197536

ER -

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