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An a posteriori error analysis for dynamic viscoelastic problems

Published online by Cambridge University Press:  26 April 2011

J. R. Fernández  and
D. Santamarina
J. R. Fernández
Affiliation:
Departamento de Matemática Aplicada I, ETSE de Telecomunicación, Universidade de Vigo, Campus As Lagoas Marcosende s/n, 36310 Vigo, Spain. [email protected]
D. Santamarina
Affiliation:
Departamento de Matemática Aplicada, Escola Politécnica Superior, Campus Univ. s/n, Universidade de Santiago de Compostela, 27002 Lugo, Spain. [email protected]
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Abstract


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

Keywords

Viscoelasticitydynamic problemsfully discrete approximationsa posteriori error estimatesfinite elementsnumerical simulations
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 45 , Issue 5 , September 2011 , pp. 925 - 945
Copyright
© EDP Sciences, SMAI, 2011

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