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Multiscale Methods and Uncertainty QuantificationPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2015 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Uppsala: Acta Universitatis Upsaliensis, 2015. , 32 p.
##### Series

Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 1287
##### Keyword [en]

multiscale methods, finite element method, discontinuous Galerkin, Petrov-Galerkin, a priori, a posteriori, complex geometry, uncertainty quantification, multilevel Monte Carlo, failure probability
##### National Category

Computational Mathematics
##### Research subject

Scientific Computing with specialization in Numerical Analysis
##### Identifiers

URN: urn:nbn:se:uu:diva-262354ISBN: 978-91-554-9336-3OAI: oai:DiVA.org:uu-262354DiVA: diva2:853534
##### Public defence

2015-10-30, Room 2446, Polacksbacken, Lägerhyddsvägen 2, Uppsala, 10:15 (English)
##### Opponent

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##### Supervisors

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#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt387",{id:"formSmash:j_idt387",widgetVar:"widget_formSmash_j_idt387",multiple:true});
Available from: 2015-10-08 Created: 2015-09-14 Last updated: 2015-10-12Bibliographically approved
##### List of papers

In this thesis we consider two great challenges in computer simulations of partial differential equations: *multiscale data*, varying over multiple scales in space and time, and *data uncertainty*, due to lack of or inexact measurements.

We develop a multiscale method based on a coarse scale correction, using localized fine scale computations. We prove that the error in the solution produced by the multiscale method decays independently of the fine scale variation in the data or the computational domain. We consider the following aspects of multiscale methods: continuous and discontinuous underlying numerical methods, adaptivity, convection-diffusion problems, Petrov-Galerkin formulation, and complex geometries.

For uncertainty quantification problems we consider the estimation of *p*-quantiles and failure probability. We use spatial a posteriori error estimates to develop and improve variance reduction techniques for Monte Carlo methods. We improve standard Monte Carlo methods for computing *p*-quantiles and multilevel Monte Carlo methods for computing failure probability.

1. An adaptive discontinuous Galerkin multiscale method for elliptic problems$(function(){PrimeFaces.cw("OverlayPanel","overlay622894",{id:"formSmash:j_idt423:0:j_idt427",widgetVar:"overlay622894",target:"formSmash:j_idt423:0:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

2. Convergence of a discontinuous Galerkin multiscale method$(function(){PrimeFaces.cw("OverlayPanel","overlay622898",{id:"formSmash:j_idt423:1:j_idt427",widgetVar:"overlay622898",target:"formSmash:j_idt423:1:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

3. A discontinuous Galerkin multiscale method for convection–diffusion problems$(function(){PrimeFaces.cw("OverlayPanel","overlay853147",{id:"formSmash:j_idt423:2:j_idt427",widgetVar:"overlay853147",target:"formSmash:j_idt423:2:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

4. On multiscale methods in Petrov–Galerkin formulation$(function(){PrimeFaces.cw("OverlayPanel","overlay785436",{id:"formSmash:j_idt423:3:j_idt427",widgetVar:"overlay785436",target:"formSmash:j_idt423:3:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

5. Multiscale methods for problems with complex geometry$(function(){PrimeFaces.cw("OverlayPanel","overlay853151",{id:"formSmash:j_idt423:4:j_idt427",widgetVar:"overlay853151",target:"formSmash:j_idt423:4:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

6. Uncertainty quantification for approximate p-quantiles for physical models with stochastic inputs$(function(){PrimeFaces.cw("OverlayPanel","overlay785381",{id:"formSmash:j_idt423:5:j_idt427",widgetVar:"overlay785381",target:"formSmash:j_idt423:5:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

7. A multilevel Monte Carlo method for computing failure probabilities$(function(){PrimeFaces.cw("OverlayPanel","overlay853139",{id:"formSmash:j_idt423:6:j_idt427",widgetVar:"overlay853139",target:"formSmash:j_idt423:6:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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