A multiscale method for linear elasticity reducing Poisson locking

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.