×

zbMATH — the first resource for mathematics

An a posteriori error analysis for dynamic viscoelastic problems. (English) Zbl 1267.74052
Summary: 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.

MSC:
74H15 Numerical approximation of solutions of dynamical problems in solid mechanics
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
74D05 Linear constitutive equations for materials with memory
74S05 Finite element methods applied to problems in solid mechanics
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
PDF BibTeX XML Cite
Full Text: DOI