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Duality-based adaptive finite element methods with application to time-dependent problemsPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2010 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Umeå: Institutionen för matematik och matematisk statistik, Umeå universitet , 2010. , p. 37
##### Series

Doctoral thesis / Umeå University, Department of Mathematics, ISSN 1102-8300 ; 45
##### Keyword [en]

finite element methods, dual-weighted residual method, multiphysics, a posteriori error estimation, adaptive algorithms, discontinuous Galerkin
##### National Category

Mathematics
##### Research subject

Mathematics
##### Identifiers

URN: urn:nbn:se:umu:diva-33872ISBN: 978-91-7459-023-4 (print)OAI: oai:DiVA.org:umu-33872DiVA, id: diva2:318503
##### Public defence

2010-06-10, MIT-huset, MA121, Umeå universitet, Umeå, 10:15 (English)
##### Opponent

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##### Supervisors

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#####

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Available from: 2010-05-11 Created: 2010-05-07 Last updated: 2010-05-24Bibliographically approved
##### List of papers

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.

1. Adaptive submodeling for linear elasticity problems with multiscale geometric features$(function(){PrimeFaces.cw("OverlayPanel","overlay318488",{id:"formSmash:j_idt480:0:j_idt484",widgetVar:"overlay318488",target:"formSmash:j_idt480:0:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

2. Simulation of multiphysics problems using adaptive finite elements$(function(){PrimeFaces.cw("OverlayPanel","overlay147783",{id:"formSmash:j_idt480:1:j_idt484",widgetVar:"overlay147783",target:"formSmash:j_idt480:1:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

3. Blockwise adaptivity for time dependent problems based on coarse scale adjoint solutions$(function(){PrimeFaces.cw("OverlayPanel","overlay318490",{id:"formSmash:j_idt480:2:j_idt484",widgetVar:"overlay318490",target:"formSmash:j_idt480:2:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

4. Adaptive finite element solution of coupled PDE-ODE systems$(function(){PrimeFaces.cw("OverlayPanel","overlay318483",{id:"formSmash:j_idt480:3:j_idt484",widgetVar:"overlay318483",target:"formSmash:j_idt480:3:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

5. A discontinuous Galerkin Nitsche method for elliptic problems with fictitious boundary$(function(){PrimeFaces.cw("OverlayPanel","overlay318485",{id:"formSmash:j_idt480:4:j_idt484",widgetVar:"overlay318485",target:"formSmash:j_idt480:4:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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