A normal compliance contact problem in viscoelasticity: An a posteriori error analysis and computational experiments |
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Authors: | JR Fernández R Martínez |
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Institution: | a Departamento de Matemática Aplicada I, Universidade de Vigo, ETSE de Telecomunicacións, Buzón 104, Campus As Lagoas Marcosende s/n, 36310 Vigo, Spainb Departamento de Matemática Aplicada, Universidade de Santiago de Compostela, Facultade de Matemáticas, Campus Vigo s/n, 15872 Santiago de Compostela, Spain |
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Abstract: | In this work, the numerical approximation of a viscoelastic contact problem is studied. The classical Kelvin-Voigt constitutive law is employed, and contact is assumed with a deformable obstacle and modelled using the normal compliance condition. The variational formulation leads to a nonlinear parabolic variational equation. An existence and uniqueness result is recalled. Then, a fully discrete scheme is introduced, by using the finite element method to approximate the spatial variable and the implicit Euler scheme to discretize time derivatives. A priori error estimates recently proved for this problem are recalled. Then, an a posteriori error analysis is provided, extending some preliminary results obtained in the study of the heat equation and other parabolic equations. Upper and lower error bounds are proved. Finally, some numerical experiments are presented to demonstrate the accuracy and the numerical behaviour of the error estimates. |
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Keywords: | 74D05 74S05 65M15 65M60 |
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