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A priori and a posteriori error analyses in the study of viscoelastic problems. (English) Zbl 1157.74039
Summary: We study the numerical approximation of a viscoelastic problem. A fully discrete scheme is introduced by using the finite element method to approximate the spatial variable, and an Euler scheme is used to discretize time derivatives. Then, two numerical analyses are presented. First, a priori estimates are proved from which the linear convergence of the algorithm is derived under suitable regularity conditions. Secondly, an a posteriori error analysis is provided extending some preliminary results obtained in the study of the heat equation. Upper and lower error bounds are obtained.

MSC:
74S05 Finite element methods applied to problems in solid mechanics
74S20 Finite difference methods applied to problems in solid mechanics
74D05 Linear constitutive equations for materials with memory
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