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On discontinuous Galerkin multiscale methods
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.
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: urn:nbn:se:uu:diva-200260OAI: oai:DiVA.org:uu-200260DiVA: diva2:622949
Supervisors
Available from: 2013-06-04 Created: 2013-05-23 Last updated: 2017-08-31Bibliographically approved
List of papers
1. Finite element multiscale methods for Poisson's equation with rapidly varying heterogeneous coefficients
Open this publication in new window or tab >>Finite element multiscale methods for Poisson's equation with rapidly varying heterogeneous coefficients
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
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-182213 (URN)
Available from: 2012-10-05 Created: 2012-10-05 Last updated: 2013-05-23Bibliographically approved
2. An adaptive discontinuous Galerkin multiscale method for elliptic problems
Open this publication in new window or tab >>An adaptive discontinuous Galerkin multiscale method for elliptic problems
2013 (English)In: Multiscale Modeling & simulation, ISSN 1540-3459, E-ISSN 1540-3467, Vol. 11, 747-765 p.Article in journal (Refereed) Published
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-200254 (URN)10.1137/120863162 (DOI)000325006000003 ()
Available from: 2013-08-01 Created: 2013-05-23 Last updated: 2017-12-06Bibliographically approved
3. Convergence of a discontinuous Galerkin multiscale method
Open this publication in new window or tab >>Convergence of a discontinuous Galerkin multiscale method
2013 (English)In: SIAM Journal on Numerical Analysis, ISSN 0036-1429, E-ISSN 1095-7170, Vol. 51, 3351-3372 p.Article in journal (Refereed) Published
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-200256 (URN)10.1137/120900113 (DOI)000328903500017 ()
Available from: 2013-12-11 Created: 2013-05-23 Last updated: 2017-12-06Bibliographically approved
4. Discontinuous Galerkin multiscale methods for convection dominated problems
Open this publication in new window or tab >>Discontinuous Galerkin multiscale methods for convection dominated problems
2013 (English)Report (Other academic)
Series
Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2013-011
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-200257 (URN)
Available from: 2013-05-23 Created: 2013-05-23 Last updated: 2013-05-23Bibliographically approved

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