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A separated representation of an error indicator for the mesh refinement process under the proper generalized decomposition framework

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Abstract

Today industries do not only require fast simulation techniques but also verification techniques for the simulations. The proper generalized decomposition (PGD) has been situated as a suitable tool for fast simulation for many physical phenomena. However, so far, verification tools for the PGD are under development. The PGD approximation error mainly comes from two different sources. The first one is related with the truncation of the PGD approximation and the second one is related with the discretization error of the underlying numerical technique. In this work we propose a fast error indicator technique based on recovery techniques, for the discretization error of the numerical technique used by the PGD technique, for refinement purposes.

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Acknowledgments

Authors 5 and 6 thank the financial support of the research Project DPI2013-46317-R of the Ministerio de Economía y Competitividad (Spain). The funding from Universitat Politècnica de València and Generalitat Valenciana (PROMETEO/2012/023) are also acknowledged. These authors also thank the support of the Framework Programme 7 Initial Training Network Funding under Grant number 289361 “Integrating Numerical Simulation and Geometric Design Technology”.

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Authors and Affiliations

  1. GEM, UMR CNRS-Centrale Nantes, 1 rue de la Noe, BP 92101, 44321, Nantes Cedex 3, France

    E. Nadal, A. Leygue & F. Chinesta

  2. Département Physique et Mécanique des Matériaux, Institut P’, ENSMA, UPR CNRS, 1 Avenue Clément Ader, BP 40109, 86961, Futuroscope Cedex, France

    M. Beringhier

  3. Centro de Investigación en Ingeniería Mecánica, Universitat Politècnica de València, Camino de Vera s/n, 46022, Valencia, Spain

    J. J. Ródenas & F. J. Fuenmayor

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  1. E. Nadal
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  2. A. Leygue
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  3. F. Chinesta
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  4. M. Beringhier
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  5. J. J. Ródenas
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  6. F. J. Fuenmayor
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Correspondence to E. Nadal.

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Nadal, E., Leygue, A., Chinesta, F. et al. A separated representation of an error indicator for the mesh refinement process under the proper generalized decomposition framework. Comput Mech 55, 251–266 (2015). https://doi.org/10.1007/s00466-014-1097-y

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  • DOI: https://doi.org/10.1007/s00466-014-1097-y

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