A multiscale method for linear elasticity reducing Poisson locking

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 Målqvist 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 Lamé parameter $\lambda$. The theoretical a priori error estimate is confirmed by numerical examples.

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• Limits to Poisson's ratio in isotropic materials
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• Polyharmonic homogenization, rough polyharmonic splines and sparse super-localization
• A localized orthogonal decomposition method for semi-linear elliptic problems
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Cited by in corpus (4)

• Computational Multiscale Methods for Linear Poroelasticity with High Contrast
• Localized Orthogonal Decomposition for two-scale Helmholtz-type problems
• A generalized finite element method for linear thermoelasticity
• Numerical upscaling of discrete network models