Abstract
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 L2-norms of the error, that are shown to convergence, for smooth solutions, as h and h2, respectively (here, h denotes the meshsize). A thorough numerical validation on a complete panel of two- and three-dimensional test cases is provided.
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