A generalized finite element method for linear thermoelasticity
Licentiatavhandling, 2016

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).

composites

local orthogonal decomposition

parabolic equations

generalized finite element

multiscale

a priori analysis

linear elasticity

Thermoelasticity

Euler
Opponent: Daniel Peterseim

Författare

Anna Persson

Göteborgs universitet

Chalmers, Matematiska vetenskaper

Ämneskategorier

Beräkningsmatematik

Euler

Opponent: Daniel Peterseim