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Article Dans Une Revue Journal of Computational and Applied Mathematics Année : 2009

A priori and a posteriori error analyses in the study of viscoelastic problems

Jose-Ramon Fernandez-Garcia
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Résumé

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.

Dates et versions

hal-00466467 , version 1 (23-03-2010)

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Jose-Ramon Fernandez-Garcia, Patrick Hild. A priori and a posteriori error analyses in the study of viscoelastic problems. Journal of Computational and Applied Mathematics, 2009, 225 (2), pp.569-580. ⟨10.1016/j.cam.2008.08.027⟩. ⟨hal-00466467⟩
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