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

Sergey Repin; Jan Valdman

Open Mathematics (2009)

  • Volume: 7, Issue: 3, page 506-519
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Sergey Repin, and Jan Valdman. "Functional a posteriori error estimates for incremental models in elasto-plasticity." Open Mathematics 7.3 (2009): 506-519. <http://eudml.org/doc/269042>.

@article{SergeyRepin2009,
abstract = {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.},
author = {Sergey Repin, Jan Valdman},
journal = {Open Mathematics},
keywords = {A posteriori error estimates; Elasto-plastic problem with isotropic hardening; Variational inequalities; a posteriori error estimates; elasto-plastic problem with isotropic hardening; variational inequalities},
language = {eng},
number = {3},
pages = {506-519},
title = {Functional a posteriori error estimates for incremental models in elasto-plasticity},
url = {http://eudml.org/doc/269042},
volume = {7},
year = {2009},
}

TY - JOUR
AU - Sergey Repin
AU - Jan Valdman
TI - Functional a posteriori error estimates for incremental models in elasto-plasticity
JO - Open Mathematics
PY - 2009
VL - 7
IS - 3
SP - 506
EP - 519
AB - 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.
LA - eng
KW - A posteriori error estimates; Elasto-plastic problem with isotropic hardening; Variational inequalities; a posteriori error estimates; elasto-plastic problem with isotropic hardening; variational inequalities
UR - http://eudml.org/doc/269042
ER -

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