A low-order nonconforming method for linear elasticity on general meshes

In this work we construct a low-order nonconforming approximation method for linear elasticity problems supporting general meshes and valid in two and three space dimensions. The method is obtained by hacking the Hybrid High-Order method of Di Pietro and Ern (2015), that requires the use of polynomials of degree k >= 1 for stability. Specifically, we show that coercivity can be recovered for k = 0 by introducing a novel term that penalises the jumps of the displacement reconstruction across mesh faces. This term plays a key role in the fulfilment of a discrete Korn inequality on broken polynomial spaces, for which a novel proof valid for general polyhedral meshes is provided. Locking-free error estimates are derived for both the energy- and the L-2-norms of the error, that are shown to convergence, for smooth solutions, as h and h(2), respectively (here, h denotes the meshsize). A thorough numerical validation on a complete panel of two-and three-dimensional test cases is provided. (C) 2019 Elsevier B.V. All rights reserved.