The proper generalized decomposition (PGD) requires separability of the input data\n(e.g. physical properties, source term, boundary conditions, initial state). In many cases\nthe input data is not expressed in a separated form and it has to be replaced by some\nseparable approximation. These approximations constitute a new error source that, in\nsome cases, may dominate the standard ones (discretization, truncation. . .) and control\nthe final accuracy of the PGD solution. In this work the relation between errors in the\nseparated input data and the errors induced in the PGD solution is discussed. Error\nestimators proposed for homogenized problems and oscillation terms are adapted to\nasses the behaviour of the PGD errors resulting from approximated input data. The PGD\nis stable with respect to error in the separated data, with no critical amplification of the\nperturbations. Interestingly, we identified a high sensitiveness of the resulting accuracy\non the selection of the sampling grid used to compute the separated data. The\nseparation has to be performed on the basis of values sampled at integration points:\nsampling at the nodes defining the functional interpolation results in an important loss\nof accuracy. For the case of a Poisson problem separated in the spatial coordinates (a\ncomplex diffusivity function requires a separable approximation), the final PGD error is\nlinear with the truncation error of the separated data. This relation is used to estimate\nthe number of terms required in the separated data, that has to be in good agreement\nwith the truncation error accepted in the PGD truncation (tolerance for the stoping\ncriteria in the enrichment procedure). A sensible choice for the prescribed accuracy of\nthe PGD solution has to be kept within the limits set by the errors in the separated\ninput data.
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