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

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, 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.

26 pages, 6 tables, and 4 Figures

References in corpus (3)

• A Hybrid High-Order method for the incompressible Navier--Stokes equations based on Temam's device
• A super--convergent hybridisable discontinuous Galerkin method for linear elasticity
• A Hybrid High-Order method for nonlinear elasticity

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