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conference paper

Analysis of linearization error for goal-oriented adaptivity of nonlinear problems

Prudhomme, Serge
•
van der Zee, Kris
•
Dede', Luca  
Moitinho de Almeida, J.P.
•
Díez, P.
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2013
Adaptive Modeling and Simulation 2013, Proceedings of the VI International Conference on Adaptive Modeling and Simulation (ADMOS 2013)
VI International Conference on Adaptive Modeling and Simulation (ADMOS 2013)

We propose in this talk to address the issue and effect of linearization in the quality of the error estimates in quantities of interest for strongly nonlinear problems. It is well known that the error representation in this case can be decomposed into two contributions: 1) one contribution in the form of the product of the residual by the solution of a linearized adjoint problem that describes the discretization error and 2) the other contribution that combines all higher-order terms with respect to the error in the primal solution that describes the linearization error. In most works on goal-oriented error estimation, the linearization error contribution is usually neglected with respect to the discretization error. However, when the nonlinear effects are significant, one cannot assume any longer that the latter is dominant over the former. In fact, it becomes obvious in those cases that linearization errors should be also controlled. We will present here the construction of refinement indicators that combine both sources of errors in order to simultaneously control those in a balanced manner.

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Type
conference paper
Author(s)
Prudhomme, Serge
van der Zee, Kris
Dede', Luca  
Editors
Moitinho de Almeida, J.P.
•
Díez, P.
•
Tiago, C.
•
Pares, N.
Date Issued

2013

Publisher

International Center for Numerical Methods in Engineering (CIMNE)

Publisher place

Barcelona, Spain

Published in
Adaptive Modeling and Simulation 2013, Proceedings of the VI International Conference on Adaptive Modeling and Simulation (ADMOS 2013)
ISBN of the book

978-84-941004-8-2

Start page

187

End page

188

Editorial or Peer reviewed

NON-REVIEWED

Written at

EPFL

EPFL units
CMCS  
Event nameEvent placeEvent date
VI International Conference on Adaptive Modeling and Simulation (ADMOS 2013)

Lisbon, Portugal

June 3-5, 2013

Available on Infoscience
November 21, 2014
Use this identifier to reference this record
https://infoscience.epfl.ch/handle/20.500.14299/109020
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