Functional a posteriori error estimates for incremental models in elasto-plasticity

• Autorzy: Sergey Repin , Jan Valdman
• Języki publikacji: EN

Abstrakty

EN

We consider incremental problem arising in elasto-plastic models with isotropic hardening. Our goal is to derive computable and guaranteed bounds of the difference between the exact solution and any function in the admissible (energy) class of the problem considered. Such estimates are obtained by an advanced version of the variational approach earlier used for linear boundary-value problems and nonlinear variational problems with convex functionals [24, 30]. They do no contain mesh-dependent constants and are valid for any conforming approximations regardless of the method used for their derivation. It is shown that the structure of error majorant reflects properties of the exact solution so that the majorant vanishes only if an approximate solution coincides with the exact one. Moreover, it possesses necessary continuity properties, so that any sequence of approximations converging to the exact solution in the energy space generates a sequence of positive numbers (explicitly computable by the majorant functional) that tends to zero.

Słowa kluczowe

EN

A posteriori error estimates; Elasto-plastic problem with isotropic hardening; Variational inequalities

Kategorie tematyczne

• 65N30: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
• 74C05: Small-strain, rate-independent theories (including rigid-plastic and elasto-plastic materials)

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2009
• Tom: 7
• Numer: 3
• Strony: 506-519

Daty

wydano

2009-09-01

online

2009-08-12

Twórcy

autor

Sergey Repin

• V.A. Steklov Institute of Mathematics in St.-Petersburg

autor

Jan Valdman

• University of Bergen

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-009-0035-2