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Error Analysis for Geometric Finite Element Discretizations of a Cosserat Rod Optimization Problem

In summary, this thesis focuses on developing an a priori theory for geometric finite element discretizations of a Cosserat rod model, which is derived from incompatible elasticity. This theory will be supported by corresponding numerical experiments to validate the convergence behavior of the proposed method.
The main result describes the qualitative behavior of intrinsic H1-errors and L2-errors in terms of the mesh diameter 0 < h ≪ 1 of the approximation scheme.
Geometric Finite Element functions uh with its subclasses Geodesic Finite Elements and Projection- based Finite Elements as conforming path-independent and objective discretizations of Cosserat rod configurations were used. Existence, regularity, variational bounds and vector field transport estimates of the Cosserat rod model were derived to ob- tain an intrinsic a-priori theory.
In the second part, this thesis concerns the derivation of the Cosserat rod from 3D elasticity featuring prestress together with numerical experiments for microheteroge- neous prestressed materials.

Identiferoai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:90662
Date08 April 2024
CreatorsBauer, Robert
ContributorsSander, Oliver, Bartels, Sören, Technische Universität Dresden
Source SetsHochschulschriftenserver (HSSS) der SLUB Dresden
LanguageEnglish
Detected LanguageEnglish
Typeinfo:eu-repo/semantics/publishedVersion, doc-type:doctoralThesis, info:eu-repo/semantics/doctoralThesis, doc-type:Text
Rightsinfo:eu-repo/semantics/openAccess

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