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

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.

References in corpus (4)

• A Hybrid High-Order method for the incompressible Navier--Stokes equations based on Temam's device
• High order exactly divergence-free Hybrid Discontinuous Galerkin Methods for unsteady incompressible flows
• A gradient-robust well-balanced scheme for the compressible isothermal Stokes problem
• Hybrid Discontinuous Galerkin methods with relaxed H(div)-conformity for incompressible flows. Part II

Cited by in corpus (2)

• HMG -- Homogeneous multigrid for HDG
• Uniform block-diagonal preconditioners for divergence-conforming HDG Methods for the generalized Stokes equations and the linear elasticity equations