Fu, Guosheng
[VerfasserIn];
Lehrenfeld, Christoph
[VerfasserIn];
Linke, Alexander
[VerfasserIn];
Streckenbach, Timo
[VerfasserIn]
;
Weierstraß-Institut für Angewandte Analysis und Stochastik
Locking free and gradient robust H(div)-conforming HDG methods for linear elasticity
Beschreibung:
Robust discretization methods for (nearly-incompressible) linear elasticity are free of volumelocking 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.