A generalized finite element method for linear thermoelasticity

TL;DR

This paper introduces a generalized finite element method for linear thermoelasticity with multiscale coefficients, achieving optimal convergence rates independent of coefficient derivatives, validated by numerical tests.

Contribution

It extends local orthogonal decomposition techniques to thermoelastic systems, providing a robust and accurate numerical method for multiscale problems.

Findings

Optimal order convergence proved

Method is independent of coefficient derivatives

Numerical examples confirm theoretical results

Abstract

We propose and analyze a generalized finite element method designed for linear quasistatic thermoelastic systems with spatial multiscale coefficients. The method is based on the local orthogonal decomposition technique introduced by M{\aa}lqvist and Peterseim (Math. Comp., 83(290): 2583--2603, 2014). We prove convergence of optimal order, independent of the derivatives of the coefficients, in the spatial $H^1$-norm. The theoretical results are confirmed by numerical examples.