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A posteriori error estimation and adaptivity for elastoplasticity using the reciprocal theorem
Author(s) -
Cirak Fehmi,
Ramm Ekkehard
Publication year - 2000
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/(sici)1097-0207(20000110/30)47:1/3<379::aid-nme776>3.0.co;2-2
Subject(s) - reciprocal , estimator , discretization error , discretization , a priori and a posteriori , mathematics , mathematical optimization , duality (order theory) , dual (grammatical number) , finite element method , variable (mathematics) , computer science , mathematical analysis , art , philosophy , linguistics , statistics , physics , literature , epistemology , discrete mathematics , thermodynamics
We present a posteriori error estimators and adaptive methods for the finite element approximation of non‐linear problems and especially elastoplasticity. The main characteristic of the proposed method is the introduction of duality techniques or in other notions the reciprocal theorem. For error estimation at an equilibrium point the non‐linear boundary value problem and an additional linearized dual problem are considered. The loading of the dual problem is specifically designed for capturing the influence of the errors of the entire domain to the considered variable. Our approach leads to easy computable refinement indicators for locally or integrally defined variables. For instationary problems as elastoplasticity, in a first step, we neglect the errors due to time discretization, and evaluate the error indicators within each time step for a stationary problem. The versatility of the presented framework is demonstrated with numerical examples. Copyright © 2000 John Wiley & Sons, Ltd.