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In this work we construct a low-order nonconforming approximation method forlinear elasticity problems supporting general meshes and valid in two and threespace dimensions. The method is obtained by hacking the Hybrid High-Ordermethod, that requires the use of polynomials of degree $k\ge1$ for stability.Specifically, we show that coercivity can be recovered for $k=0$ by introducinga novel term that penalises the jumps of the displacement reconstruction acrossmesh faces. This term plays a key role in the fulfillment of a discrete Korninequality on broken polynomial spaces, for which a novel proof valid forgeneral polyhedral meshes is provided. Locking-free error estimates are derivedfor both the energy- and the $L^2$-norms of the error, that are shown toconvergence, for smooth solutions, as $h$ and $h^2$, respectively (here, $h$denotes the meshsize). A thorough numerical validation on a complete panel oftwo- and three-dimensional test cases is provided.

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