A mixed generalized multiscale finite element method for planar linear elasticity

A mixed generalized multiscale finite element method for linear elasticity based on. Hellinger Reissner principle with a strong symmetry enforcement for the stress tensor is introduced. The multiscale approximation space for the stress tensor is built on a coarse grid with carefully designed local problems so that the basis functions are also symmetric. Using eigenfunctions of local spectral problems as basis functions allows the approximation error of the multiscale finite element space to have a rapid spectral decay. Together with a properly chosen approximation space for the displacement, the method is shown to be inf-sup stable and robust as the first Lame coefficient lambda -> infinity. Numerical experiments are supplemented to demonstrate fast convergence of the method with respect to local enrichment, and robustness of the method with respect to high contrast heterogeneity of the Poisson ratio. (C) 2018 Elsevier B.V. All rights reserved.