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Finite element multiscale methods for Poisson's equation with rapidly varying heterogeneous coefficients
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
2012 (English)In: Proc. 10th World Congress on Computational Mechanics, Barcelona, Spain: International Association for Computational Mechanics , 2012, 10- p.Conference paper, Published paper (Refereed)
Place, publisher, year, edition, pages
Barcelona, Spain: International Association for Computational Mechanics , 2012. 10- p.
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-182213OAI: oai:DiVA.org:uu-182213DiVA: diva2:558870
Available from: 2012-10-05 Created: 2012-10-05 Last updated: 2013-05-23Bibliographically approved
In thesis
1. On discontinuous Galerkin multiscale methods
Open this publication in new window or tab >>On discontinuous Galerkin multiscale methods
2013 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

In this thesis a new multiscale method, the discontinuous Galerkin multiscale method, is proposed. The method uses localized fine scale computations to correct a global coarse scale equation and thereby takes the fine scale features into account. We show a priori error bounds for convection dominated diffusion-convection-reaction problems with variable coefficients. We also present a posteriori error bound in the case of no convection or reaction and present an adaptive algorithm which tunes the method parameters automatically. We also present extensive numerical experiments which verify our analytical findings.

Place, publisher, year, edition, pages
Uppsala University, 2013
Series
Information technology licentiate theses: Licentiate theses from the Department of Information Technology, ISSN 1404-5117 ; 2013-003
National Category
Computational Mathematics
Research subject
Scientific Computing with specialization in Numerical Analysis
Identifiers
urn:nbn:se:uu:diva-200260 (URN)
Supervisors
Available from: 2013-06-04 Created: 2013-05-23 Last updated: 2017-08-31Bibliographically approved

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Elfverson, DanielMålqvist, Axel

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