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Adaptive submodeling for linear elasticity problems with multiscale geometric features
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2005 (English)In: Multiscale Methods in Science and Engineering / [ed] Björn Engquist, Olof Runborg and Per Lötstedt, Berlin Heidelberg: Springer Verlag , 2005, Vol. 44, 169-180 p.Chapter in book (Other academic)
Abstract [en]

Submodeling is a procedure for local enhancement of the resolution of a coarse global finite element solution by solving a local problem on a subdomain containing an area of particular interest. We focus on linear elasticity and computation of local stress levels determined by the local geometry of the domain. We derive a posteriori error estimates for the submodeling procedure using duality techniques. Based on these estimates we propose an adaptive procedure for automatic choice of the resolution and size of the submodel. The procedure is illustrated for problems of industrial interest.

Place, publisher, year, edition, pages
Berlin Heidelberg: Springer Verlag , 2005. Vol. 44, 169-180 p.
Series
Lecture notes in Computational Science and Engineering, ISSN 1439-7358 ; 44
Keyword [en]
adaptive multiscale method, a posteriori error estimate, finite element, meshrefinement
National Category
Computational Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-33869DOI: 10.1007/b137594ISBN: 978-3-540-25335-8 (Print) 978-3-540-26444-6 (Online) OAI: oai:DiVA.org:umu-33869DiVA: diva2:318488
Available from: 2010-05-07 Created: 2010-05-07 Last updated: 2010-05-24Bibliographically approved
In thesis
1. Duality-based adaptive finite element methods with application to time-dependent problems
Open this publication in new window or tab >>Duality-based adaptive finite element methods with application to time-dependent problems
2010 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

To simulate real world problems modeled by differential equations, it is often not sufficient to  consider and tackle a single equation. Rather, complex phenomena are modeled by several partial dierential equations that are coupled to each other. For example, a heart beat involve electric activity, mechanics of the movement of the walls and valves, as well as blood fow - a true multiphysics problem. There may also be ordinary differential equations modeling the reactions on a cellular level, and these may act on a much finer scale in both space and time. Determining efficient and accurate simulation tools for such multiscalar multiphysics problems is a challenge.

The five scientific papers constituting this thesis investigate and present solutions to issues regarding accurate and efficient simulation using adaptive finite element methods. These include handling local accuracy through submodeling, analyzing error propagation in time-dependent  multiphysics problems, developing efficient algorithms for adaptivity in time and space, and deriving error analysis for coupled PDE-ODE systems. In all these examples, the error is analyzed and controlled using the framework of dual-weighted residuals, and the spatial meshes are handled using octree based data structures. However, few realistic geometries fit such grid and to address this issue a discontinuous Galerkin Nitsche method is presented and analyzed.

Place, publisher, year, edition, pages
Umeå: Institutionen för matematik och matematisk statistik, Umeå universitet, 2010. 37 p.
Series
Doctoral thesis / Umeå University, Department of Mathematics, ISSN 1102-8300 ; 45
Keyword
finite element methods, dual-weighted residual method, multiphysics, a posteriori error estimation, adaptive algorithms, discontinuous Galerkin
National Category
Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:umu:diva-33872 (URN)978-91-7459-023-4 (ISBN)
Public defence
2010-06-10, MIT-huset, MA121, Umeå universitet, Umeå, 10:15 (English)
Opponent
Supervisors
Available from: 2010-05-11 Created: 2010-05-07 Last updated: 2010-05-24Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
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