Locking free and gradient robust H(div)-conforming HDG methods for linear elasticity
- Fu, Guosheng
- Lehrenfeld, Christoph
- Linke, Alexander
- Streckenbach, Timo
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.
- J. Sci. Comput., 86 (2021), DOI 10.1007/s10915-020-01396-6 .