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

[EN] 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. Authors 5 and 6 thank the financial support of the research Project DPI2013-46317-R of the Ministerio de Economia y Competitividad (Spain). The funding from Universitat Politecnica de Valencia 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". Nadal, E.; Leygue, A.; Chinesta, F.; Beringhier, M.; Ródenas, J.; Fuenmayor Fernández, FJ. (2015). A separated representation of an error indicator for the mesh refinement process under the proper generalized decomposition framework. Computational Mechanics. 55(2):251-266. https://doi.org/10.1007/s00466-014-1097-y Ammar A, Mokdad B, Chinesta F, Keunings R (2006) A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modeling of complex fluids. J Non-Newton Fluid Mech 139:153–176 Ammar A, Mokdad B, Chinesta F, Keunings R (2007) A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modelling of complex fluids. J Non-Newton Fluid Mech 144:98–121 Chinesta F, Ladeveze P, Cueto E (2011) A short review on model order reduction based on proper generalized decomposition. Arch Comput Methods Eng 18:395–404 Giner E, Bognet B, Ródenas JJ, Leygue A, Fuenmayor FJ, Chinesta F (2013) The proper generalized decomposition (PGD) as a numerical procedure to solve 3D cracked plates in linear elastic fracture mechanics. Int J Solids Struct 50:1710–1720 Chinesta F, Ammar A, Leygue A, Keunings R (2011) An overview of the proper generalized decomposition with