MATHICSE Technical Report : A quasi-optimal sparse grids procedure for groundwater flows
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| Titel: | MATHICSE Technical Report : A quasi-optimal sparse grids procedure for groundwater flows |
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| Autoren: | Beck, Joakim, Nobile, Fabio, Tamellini, Lorenzo, Tempone, Raúl |
| Weitere Verfasser: | MATHICSE-Group |
| Verlagsinformationen: | MATHICSE Écublens |
| Publikationsjahr: | 2019 |
| Bestand: | Ecole Polytechnique Fédérale Lausanne (EPFL): Infoscience |
| Schlagwörter: | Uncertainty Quantification, PDEs with random data, linear elliptic equations, Darcy equation, lognormal permeability, Karhunen-Loève, Stochastic Collocation methods, Sparse grids approximation |
| Beschreibung: | In this work we explore the extension of the quasi-optimal sparse grids method proposed in our previous work \On the optimal polynomial ap- proximation of stochastic PDEs by Galerkin and Collocation methods" to a Darcy problem where the permeability is modeled as a lognormal random field. We propose an explicit a-priori/a-posteriori procedure for the construc- tion of such quasi-optimal grid and show its effectivenenss on a numerical ex- ample. In this approach, the two main ingredients are an estimate of the decay of the Hermite coefficients of the solution and ; CSQI ; MATHICSE Technical Report Nr. 46.2012 November 2012 |
| Publikationsart: | report |
| Sprache: | unknown |
| Relation: | https://infoscience.epfl.ch/record/263218/files/46.2012_JB-FN-LT-RT.pdf; #PLACEHOLDER_PARENT_METADATA_VALUE#; https://infoscience.epfl.ch/handle/20.500.14299/153689 |
| DOI: | 10.5075/epfl-MATHICSE-263218 |
| Verfügbarkeit: | https://doi.org/10.5075/epfl-MATHICSE-263218 https://infoscience.epfl.ch/handle/20.500.14299/153689 https://hdl.handle.net/20.500.14299/153689 |
| Dokumentencode: | edsbas.23537318 |
| Datenbank: | BASE |
Nájsť tento článok vo Web of Science | Abstract: | In this work we explore the extension of the quasi-optimal sparse grids method proposed in our previous work \On the optimal polynomial ap- proximation of stochastic PDEs by Galerkin and Collocation methods" to a Darcy problem where the permeability is modeled as a lognormal random field. We propose an explicit a-priori/a-posteriori procedure for the construc- tion of such quasi-optimal grid and show its effectivenenss on a numerical ex- ample. In this approach, the two main ingredients are an estimate of the decay of the Hermite coefficients of the solution and ; CSQI ; MATHICSE Technical Report Nr. 46.2012 November 2012 |
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| DOI: | 10.5075/epfl-MATHICSE-263218 |