Locking free and gradient robust H(div)-conforming HDG methods for linear elasticity

TL;DR

This paper introduces novel HDG methods for linear elasticity that are both free of volume-locking and gradient-robust, ensuring accurate and efficient simulations of nearly-incompressible materials.

Contribution

The paper proposes new divergence-conforming HDG methods that are gradient-robust and free of volume-locking, including relaxed divergence-conformity variants for improved efficiency.

Findings

Methods are gradient-robust and free of volume-locking.

Discretizations achieve quasi-optimal convergence.

Enhanced computational efficiency with relaxed conformity.

Abstract

Robust discretization methods for (nearly-incompressible) linear elasticity are free of volume-locking and gradient-robust. While volume-locking is a well-known problem that can be dealt with in many different discretization approaches, the concept of gradient-robustness for linear elasticity is new. We discuss both aspects and propose novel Hybrid Discontinuous Galerkin (HDG) methods for linear elasticity. The starting point for these methods is a divergence-conforming discretization. As a consequence of its well-behaved Stokes limit the method is gradient-robust and free of volume-locking. To improve computational efficiency, we additionally consider discretizations with relaxed divergence-conformity and a modification which re-enables gradient-robustness, yielding a robust and quasi-optimal discretization also in the sense of HDG superconvergence.