A generalized finite element method for linear thermoelasticity
Licentiate thesis, 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).

a priori analysis

Thermoelasticity

linear elasticity

generalized finite element

parabolic equations

local orthogonal decomposition

composites

multiscale

Euler
Opponent: Daniel Peterseim

Author

Anna Persson

Chalmers, Mathematical Sciences

University of Gothenburg

Multiscale techniques for parabolic equations

Numerische Mathematik,; Vol. 138(2018)p. 191-217

Journal article

A multiscale method for linear elasticity reducing Poisson locking

Computer Methods in Applied Mechanics and Engineering,; Vol. 310(2016)p. 156-171

Journal article

A Generalized Finite Element Method for Linear Thermoelasticity

Mathematical Modelling and Numerical Analysis,; Vol. 51(2017)p. 1145-1171

Journal article

Subject Categories

Computational Mathematics

Publisher

Chalmers University of Technology

Euler

Opponent: Daniel Peterseim

More information

Latest update

2/3/2020 8