Convergence of adaptive stochastic collocation with finite elements
Abstract:
We consider an elliptic partial differential equation with a random diffusion parameter discretized by a stochastic collocation method in the parameter domain and a finite element method in the spatial domain. We prove for the first time convergence of a stochastic collocation algorithm which adaptively enriches the parameter space as well as refines the finite element meshes.
| Zugehörige Institution(en) am KIT | Sonderforschungsbereich 1173 (SFB 1173) |
| Publikationstyp | Forschungsbericht/Preprint |
| Publikationsmonat/-jahr | 11.2020 |
| Sprache | Englisch |
| Identifikator | ISSN: 2365-662X KITopen-ID: 1000125783 |
| Verlag | Karlsruher Institut für Technologie (KIT) |
| Umfang | 26 S. |
| Serie | CRC 1173 Preprint ; 2020/34 |
| Projektinformation | SFB 1173/2 (DFG, DFG KOORD, SFB 1173/2 2019) |
| Externe Relationen | Siehe auch |
| Schlagwörter | uncertainty quantification, adaptive algorithm, high dimensional approximation, sparse grids, finite element method |