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A continuous/discontinuous Galerkin method for the biharmonic problem on surfacesPrimeFaces.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}); (English)Manuscript (preprint) (Other academic)
##### Abstract [en]

##### National Category

Computational Mathematics
##### Identifiers

URN: urn:nbn:se:umu:diva-79207OAI: oai:DiVA.org:umu-79207DiVA: diva2:640280
#####

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Available from: 2013-08-13 Created: 2013-08-13 Last updated: 2013-08-14Bibliographically approved
##### In thesis

We present a continuous/discontinuous Galerkin method for approximating solutions to a fourth order elliptic PDE on a surface embedded in R^{3}. A priori error estimates, taking both the approximation of the surface andthe approximation of surface differential operators into account, are proven in a discrete energy norm and in L^{2}-norm. This can be seen as an extension of the formalism and method originally used in [Dzi88] for approximatingsolutions to the Laplace-Beltrami problem. Using a polyhedral approximation Σ_{h} of an implicitly defined surface Σ embedded in R^{3} we employ continuous piecewise quadratic finite elements to approximate solutions to the biharmonic equation on Σ. Numerical examples on the sphere and on the torus confirm the convergence rate implied by our estimates.

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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