Multiscale Methods and Uncertainty Quantification
2015 (English)Doctoral thesis, comprehensive summary (Other academic)
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.
Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2015. , 32 p.
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 1287
multiscale methods, finite element method, discontinuous Galerkin, Petrov-Galerkin, a priori, a posteriori, complex geometry, uncertainty quantification, multilevel Monte Carlo, failure probability
Research subject Scientific Computing with specialization in Numerical Analysis
IdentifiersURN: urn:nbn:se:uu:diva-262354ISBN: 978-91-554-9336-3OAI: oai:DiVA.org:uu-262354DiVA: diva2:853534
2015-10-30, Room 2446, Polacksbacken, Lägerhyddsvägen 2, Uppsala, 10:15 (English)
Legoll, Frédéric, Professor
Målqvist, Axel, Docent
List of papers