A multiscale method for linear elasticity reducing Poisson locking

TL;DR

This paper introduces a multiscale finite element method for linear elasticity with highly oscillating coefficients, achieving linear convergence and effectively handling materials with large Lamé parameters.

Contribution

It extends localized orthogonal decomposition techniques to linear elasticity, providing a generalized finite element method that converges linearly under minimal regularity assumptions.

Findings

Proven linear convergence in the H^1-norm.

Numerical examples confirm theoretical error estimates.

Effective for materials with large Lamé parameters.

Abstract

We propose a generalized finite element method for linear elasticity equations with highly varying and oscillating coefficients. The method is formulated in the framework of localized orthogonal decomposition techniques introduced by M{\aa}lqvist and Peterseim (Math. Comp., 83(290): 2583--2603, 2014). Assuming only $L_\infty$-coefficients we prove linear convergence in the $H^1$-norm, also for materials with large Lam\'{e} parameter $\lambda$. The theoretical a priori error estimate is confirmed by numerical examples.