LAUSR

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, CMAME, 2015, 283:1-21], that requires the use of polynomials of degree $k\ge 1$ 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 fulfillment 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.