Towards simplified and optimized a posteriori error estimation using PGD reduced models

Summary The paper deals with the use of model order reduction within a posteriori error estimation procedures in the context of the finite element method. More specifically, it focuses on the constitutive relation error concept, which has been widely used over the last 40 years for FEM verification...

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Bibliographic Details
Published in:International journal for numerical methods in engineering 2018-02, Vol.113 (6), p.967-998
Main Authors: Allier, Pierre‐Eric, Chamoin, Ludovic, Ladevèze, Pierre
Format: Article
Language:English
Subjects:
constitutive relation error
Constitutive relationships
Decomposition
Engineering Sciences
Error analysis
error estimation
Finite element method
finite element methods
Mathematical models
Mathematics
Mechanics
Model reduction
Nonlinear programming
Numerical Analysis
Program verification (computers)
proper generalized decomposition
Upper bounds
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Summary:Summary The paper deals with the use of model order reduction within a posteriori error estimation procedures in the context of the finite element method. More specifically, it focuses on the constitutive relation error concept, which has been widely used over the last 40 years for FEM verification of computational mechanics models. A technical key‐point when using constitutive relation error is the construction of admissible fields, and we propose here to use the proper generalized decomposition to facilitate this task. In addition to making the implementation into commercial FE software easier, it is shown that the use of proper generalized decomposition enables to optimize the verification procedure and to get both accurate and reasonably expensive upper bounds on the discretization error. Numerical illustrations are presented to assess the performance of the proposed approach.
ISSN:0029-5981
1097-0207
DOI:10.1002/nme.5695