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A priori and a posteriori error analyses in the study of viscoelastic problems
Authors:J.R. Ferná  ndez,P. Hild
Affiliation:1. Departamento de Matemática Aplicada, Universidade de Santiago de Compostela, Facultade de Matemáticas, Campus Universitario Sur s/n, 15782 Santiago de Compostela, Spain;2. Laboratoire de Mathématiques de Besançon, Université de Franche-Comté, UMR CNRS 6623, 16 route de Gray, 25030 Besançon, France
Abstract:
In this work, the numerical approximation of a viscoelastic problem is studied. 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. 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.
Keywords:74D05   74S05   65M15   65M60
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