An intrinsic Proper Generalized Decomposition for parametric symmetric elliptic problems
| hal.structure.identifier | Institut de Mécanique et d'Ingénierie de Bordeaux [I2M] | |
| dc.contributor.author | AZAIEZ, Mejdi | |
| hal.structure.identifier | Université de Technologie de Compiègne [UTC] | |
| dc.contributor.author | BEN BELGACEM, Faker | |
| hal.structure.identifier | Departamento de Ecuaciones Diferenciales y Analisis Numerico [EDAN US] | |
| dc.contributor.author | CASADO-DIAZ, Juan | |
| hal.structure.identifier | Departamento de Ecuaciones Diferenciales y Analisis Numerico [EDAN US] | |
| dc.contributor.author | CHACON REBOLLO, Tomas | |
| hal.structure.identifier | Laboratoire Jacques-Louis Lions [LJLL] | |
| dc.contributor.author | MURAT, François | |
| dc.date.accessioned | 2021-05-14T09:50:45Z | |
| dc.date.available | 2021-05-14T09:50:45Z | |
| dc.date.created | 2017-06 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/77313 | |
| dc.description.abstractEn | We introduce in this paper a technique for the reduced order approximation of parametric symmetric elliptic partial differential equations. For any given dimension, we prove the existence of an optimal subspace of at most that dimension which realizes the best approximation in mean of the error with respect to the parameter in the quadratic norm associated to the elliptic operator between the exact solution and the Galerkin solution calculated on the subspace. This is analogous to the best approximation property of the Proper Orthogonal Decomposition (POD) subspaces, excepting that in our case the norm is parameter-depending, and then the POD optimal sub-spaces cannot be characterized by means of a spectral problem. We apply a deflation technique to build a series of approximating solutions on finite-dimensional optimal subspaces, directly in the on-line step. We prove that the partial sums converge to the continuous solutions in mean quadratic elliptic norm. | |
| dc.language.iso | en | |
| dc.title.en | An intrinsic Proper Generalized Decomposition for parametric symmetric elliptic problems | |
| dc.type | Document de travail - Pré-publication | |
| dc.subject.hal | Mathématiques [math]/Equations aux dérivées partielles [math.AP] | |
| dc.subject.hal | Mathématiques [math]/Analyse numérique [math.NA] | |
| bordeaux.hal.laboratories | Institut de Mécanique et d’Ingénierie de Bordeaux (I2M) - UMR 5295 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.institution | INRAE | |
| bordeaux.institution | Arts et Métiers | |
| hal.identifier | hal-01557190 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01557190v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=AZAIEZ,%20Mejdi&BEN%20BELGACEM,%20Faker&CASADO-DIAZ,%20Juan&CHACON%20REBOLLO,%20Tomas&MURAT,%20Fran%C3%A7ois&rft.genre=preprint |
Fichier(s) constituant ce document
| Fichiers | Taille | Format | Vue |
|---|---|---|---|
|
Il n'y a pas de fichiers associés à ce document. |
|||