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A discontinuous galerkin multiscale method for first order hyperbolic equations
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Department of Information Technology, Uppsala.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
(English)Manuscript (preprint) (Other academic)
Identifiers
URN: urn:nbn:se:umu:diva-42711OAI: oai:DiVA.org:umu-42711DiVA: diva2:410022
Available from: 2011-04-12 Created: 2011-04-12 Last updated: 2011-04-14Bibliographically approved
In thesis
1. Finite element methods for multiscale/multiphysics problems
Open this publication in new window or tab >>Finite element methods for multiscale/multiphysics problems
2011 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

In this thesis we focus on multiscale and multiphysics problems. We derive a posteriori error estimates for a one way coupled multiphysics problem, using the dual weighted residual method. Such estimates can be used to drive local mesh refinement in adaptive algorithms, in order to efficiently obtain good accuracy in a desired goal quantity, which we demonstrate numerically. Furthermore we prove existence and uniqueness of finite element solutions for a two way coupled multiphysics problem. The possibility of deriving dual weighted a posteriori error estimates for two way coupled problems is also addressed. For a two way coupled linear problem, we show numerically that unless the coupling of the equations is to strong the propagation of errors between the solvers goes to zero.

We also apply a variational multiscale method to both an elliptic and a hyperbolic problem that exhibits multiscale features. The method is based on numerical solutions of decoupled local fine scale problems on patches. For the elliptic problem we derive an a posteriori error estimate and use an adaptive algorithm to automatically tune the resolution and patch size of the local problems. For the hyperbolic problem we demonstrate the importance of how to construct the patches of the local problems, by numerically comparing the results obtained for symmetric and directed patches.

Place, publisher, year, edition, pages
Umeå: Department of Mathematics and Mathematical Statistics, Umeå University, 2011. 26 p.
Series
Doctoral thesis / Umeå University, Department of Mathematics, ISSN 1102-8300 ; 47
Keyword
finite element methods, variational multiscale methods, Galerkin, convergence analysis, multiphysics, a posteriori error estimation, duality, adaptivity
National Category
Probability Theory and Statistics
Research subject
Mathematical Statistics
Identifiers
urn:nbn:se:umu:diva-42713 (URN)978-91-7459-193-4 (ISBN)
Public defence
2011-05-05, MIT-huset, MA121, Umeå universitet, Umeå, 10:15 (English)
Opponent
Supervisors
Available from: 2011-04-14 Created: 2011-04-12 Last updated: 2011-04-14Bibliographically approved

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Larson, Mats G.Söderlund, Robert

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CiteExportLink to record
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Citation style
  • apa
  • ieee
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  • de-DE
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