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Analysis of a one‐dimensional damage model
Author(s) -
Fernández José R.
Publication year - 2005
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20081
Subject(s) - discretization , mathematics , backward euler method , quadrature (astronomy) , finite element method , euler method , convergence (economics) , numerical analysis , partial derivative , displacement (psychology) , mathematical analysis , partial differential equation , work (physics) , euler's formula , physics , psychology , economics , psychotherapist , economic growth , optics , thermodynamics
In this work, a one‐dimensional model for the evolution of the damage of an elastic material caused by tension is considered. The model consists of a coupled set of differential inclusions for the elastic displacement and the damage fields. The model decouples, and once the damage is found, the elastic deformations are obtained by quadrature. The existence of a unique solution was proved in Frémond et al. Here, we deal with the numerical analysis of this problem. Using the finite element method to approximate the spatial variable and the backward Euler scheme to discretize the time derivatives, a numerical algorithm is proposed. Error estimates are derived and, under suitable regularity hypotheses, the linear convergence of the numerical scheme deduced. We conclude with some numerical simulations. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005