A priori and a posteriori error analysis of finite element methods for plate models

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dc.contributor Aalto-yliopisto fi
dc.contributor Aalto University en
dc.contributor.author Niiranen, Jarkko
dc.date.accessioned 2012-02-24T08:44:14Z
dc.date.available 2012-02-24T08:44:14Z
dc.date.issued 2007-11-09
dc.identifier.isbn 978-951-22-9004-8
dc.identifier.issn 0784-3143
dc.identifier.uri https://aaltodoc.aalto.fi/handle/123456789/2940
dc.description.abstract The focus of this dissertation is in the theoretical and computational analysis of the discretization error indused by finite element methods for plate problems. For the Reissner–Mindlin plate model, regularity results with respect to the loading and a priori convergence estimates for the MITC finite elements are presented. The convergence results are valid uniformly with respect to the thickness parameter. In addition, we prove a local superconvergence result for the deflection approximation of MITC elements, and introduce a postprocessing method improving the accuracy of the approximation. The convergence results are confirmed by numerical computations. For the Kirchhoff–Love plate model, a new family of C0-continuous, optimally convergent finite elements is introduced. Furthermore, we derive a reliable and efficient a posteriori error indicator and verify the results by benchmark computations. Another a posteriori error analysis is performed for the Morley plate element. en
dc.description.abstract Väitöskirjassa analysoidaan sekä teoreettisesti että laskennallisesti laattamalleille kehiteltyjen elementtimenetelmien diskretointivirhettä. Reissner–Mindlin-laattamallille esitetään kuormituksen suhteen lausuttuja säännöllisyystuloksia ja MITC-laattaelementtien a priori -virhearvioita. Suppenemistulokset ovat voimassa laatan paksuusparametrin suhteen tasaisesti. Lisäksi MITC-elementtien taipuma-approksimaatiolle todistetaan lokaali superkonvergenssitulos ja esitetään approksimaation tarkkuutta parantava jälkikäsittelymenetelmä. Suppenemistulokset vahvistetaan numeerisilla esimerkeillä. Kirchhoff–Love-laattamallille esitetään uusi C0-jatkuva, optimaalisesti suppeneva elementtiperhe. Näille elementeille johdetaan luotettava ja tehokas a posteriori -virheindikaattori ja tulokset verifioidaan numeerisesti. Lisäksi suoritetaan a posteriori -virheanalyysi Morleyn laattaelementille. fi
dc.format.extent 27, [app]
dc.format.mimetype application/pdf
dc.language.iso en en
dc.publisher Helsinki University of Technology en
dc.publisher Teknillinen korkeakoulu fi
dc.relation.ispartofseries Research reports / Helsinki University of Technology, Institute of Mathematics. A en
dc.relation.ispartofseries 534 en
dc.relation.haspart Mikko Lyly, Jarkko Niiranen, Rolf Stenberg. A refined error analysis of MITC plate elements. Mathematical Models and Methods in Applied Sciences, 16 (2006), 967-977.
dc.relation.haspart Mikko Lyly, Jarkko Niiranen, Rolf Stenberg. Superconvergence and postprocessing of MITC plate elements. Computer Methods in Applied Mechanics and Engineering, 196 (2007), 3110-3126.
dc.relation.haspart Lourenço Beirão da Veiga, Jarkko Niiranen, Rolf Stenberg. A family of C0 finite elements for Kirchhoff plates I: Error analysis. SIAM Journal on Numerical Analysis, 45 (2007), 2047-2071. [article3.pdf] © 2007 Society for Industrial and Applied Mathematics (SIAM). By permission.
dc.relation.haspart Lourenço Beirão da Veiga, Jarkko Niiranen, Rolf Stenberg. A family of C0 finite elements for Kirchhoff plates II: Numerical results. Helsinki University of Technology, Institute of Mathematics, Research Reports, A526 (2007), 29 pages. Computer Methods in Applied Mechanics and Engineering, accepted for publication. [article4.pdf] © 2007 by authors and © 2007 Elsevier Science. By permission.
dc.relation.haspart Lourenço Beirão da Veiga, Jarkko Niiranen, Rolf Stenberg. A posteriori error estimates for the Morley plate bending element. Numerische Mathematik, 106 (2007), 165-179. [article5.pdf] © 2007 Springer Science+Business Media. By permission.
dc.subject.other Mathematics en
dc.title A priori and a posteriori error analysis of finite element methods for plate models en
dc.title A priori- ja a posteriori -virheanalyysi laattamallien elementtimenetelmille fi
dc.type G5 Artikkeliväitöskirja fi
dc.description.version reviewed en
dc.contributor.department Department of Engineering Physics and Mathematics en
dc.contributor.department Teknillisen fysiikan ja matematiikan osasto fi
dc.subject.keyword finite elements en
dc.subject.keyword a priori error analysis en
dc.subject.keyword a posteriori error analysis en
dc.subject.keyword plate models en
dc.subject.keyword MITC-elements en
dc.subject.keyword adaptivity en
dc.subject.keyword elementtimenetelmä fi
dc.subject.keyword a priori -virheanalyysi fi
dc.subject.keyword a posteriori -virheanalyysi fi
dc.subject.keyword laattamallit fi
dc.subject.keyword MITC-elementit fi
dc.subject.keyword adaptiivisuus fi
dc.identifier.urn urn:nbn:fi:tkk-010686
dc.type.dcmitype text en
dc.type.ontasot Väitöskirja (artikkeli) fi
dc.type.ontasot Doctoral dissertation (article-based) en
dc.contributor.lab Institute of Mathematics en
dc.contributor.lab Matematiikan laitos fi


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