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Continuous piecewise linear finite elements for the Kirchhoff–Love plate equationPrimeFaces.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}); 2012 (English)In: Numerische Mathematik, ISSN 0029-599X, E-ISSN 0945-3245, Vol. 121, no 1, 65-97 p.Article in journal (Refereed) Published
##### Abstract [en]

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

Springer Berlin/Heidelberg, 2012. Vol. 121, no 1, 65-97 p.
##### National Category

Computational Mathematics
##### Identifiers

URN: urn:nbn:se:umu:diva-50810DOI: 10.1007/s00211-011-0429-5ISI: 000302749600003OAI: oai:DiVA.org:umu-50810DiVA: diva2:473342
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Available from: 2012-01-05 Created: 2011-12-22 Last updated: 2015-06-03Bibliographically approved
##### In thesis

A family of continuous piecewise linear finite elements for thin plate problems is presented. We use standard linear interpolation of the deflection field to reconstruct a discontinuous piecewise quadratic deflection field. This allows us to use discontinuous Galerkin methods for the Kirchhoff–Love plate equation. Three example reconstructions of quadratic functions from linear interpolation triangles are presented: a reconstruction using Morley basis functions, a fully quadratic reconstruction, and a more general least squares approach to a fully quadratic reconstruction. The Morley reconstruction is shown to be equivalent to the basic plate triangle (BPT). Given a condition on the reconstruction operator, a priori error estimates are proved in energy norm and *L*^{2} norm. Numerical results indicate that the Morley reconstruction/BPT does not converge on unstructured meshes while the fully quadratic reconstruction show optimal convergence.

1. Finite Element Methods for Thin Structures with Applications in Solid Mechanics$(function(){PrimeFaces.cw("OverlayPanel","overlay640426",{id:"formSmash:j_idt647:0:j_idt651",widgetVar:"overlay640426",target:"formSmash:j_idt647:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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