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Göteborgs universitets publikationer

A generalized finite element method for linear thermoelasticity

Författare och institution:
Anna Persson (Institutionen för matematiska vetenskaper, Chalmers/GU)
Antal sidor:
118
Publikationstyp:
Licentiatavhandling
Förlag:
Chalmers University of Technology
Förlagsort:
Göteborg
Publiceringsår:
2016
Språk:
engelska
Datum för examination:
2016-05-27
Tidpunkt för examination:
10:15
Lokal:
Euler
Opponent:
Daniel Peterseim
Fulltextlänk (lokalt arkiv):
Sammanfattning (abstract):
In this thesis we develop a generalized finite element method for linear thermoelasticity problems, modeling displacement and temperature in an elastic body. We focus on strongly heterogeneous materials, like composites. For classical finite element methods such problems are known to be numerically challenging due to the rapid variations in the data. The method we propose is based on the local orthogonal decomposition technique introduced by M{\aa}lqvist and Peterseim (Math. Comp., 83(290): 2583--2603, 2014). In short, the idea is to enrich the classical finite element nodal basis function using information from the diffusion coefficient. Locally, these basis functions have better approximation properties than the nodal basis functions. The papers included in this thesis first extends the local orthogonal decomposition framework to parabolic problems (Paper I) and to linear elasticity equations (Paper II). Finally, using the theory developed in these papers, we address the linear thermoelastic system (Paper III).
Ämne (baseras på Högskoleverkets indelning av forskningsämnen):
NATURVETENSKAP ->
Matematik ->
Beräkningsmatematik ->
Tillämpad matematik ->
Numerisk analys
Nyckelord:
Thermoelasticity, parabolic equations, linear elasticity, multiscale, composites, generalized finite element, local orthogonal decomposition, a priori analysis
Postens nummer:
235750
Posten skapad:
2016-05-02 09:56
Posten ändrad:
2016-05-11 08:53

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