WIAS Preprint No. 2680, (2020)

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


  • Fu, Guosheng
  • Lehrenfeld, Christoph
  • Linke, Alexander
    ORCID: 0000-0002-0165-2698
  • Streckenbach, Timo
    ORCID: 0009-0001-0874-0463

2010 Mathematics Subject Classification

  • 65N30 65N12 74B05 76D07


  • Linear elasticity, nearly incompressible, locking phenomenon, volume-locking, gradient-robustness, discontinuous Galerkin, H(div)-conforming HDG methods




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.

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