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A posteriori error estimation and adaptivity for elastoplasticity using the reciprocal theorem

✍ Scribed by Fehmi Cirak; Ekkehard Ramm

Publisher
John Wiley and Sons
Year
2000
Tongue
English
Weight
231 KB
Volume
47
Category
Article
ISSN
0029-5981

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✦ Synopsis

We present a posteriori error estimators and adaptive methods for the ÿnite element approximation of nonlinear 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 speciÿcally designed for capturing the in uence of the errors of the entire domain to the considered variable. Our approach leads to easy computable reÿnement indicators for locally or integrally deÿned variables. For instationary problems as elastoplasticity, in a ÿrst 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.

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