论文标题
锁定免费和梯度强大的H（DIV） - 合并线性弹性的HDG方法
Locking free and gradient robust H(div)-conforming HDG methods for linear elasticity
论文作者
论文摘要
（几乎不可压缩）线性弹性的鲁棒离散方法无体积锁定和梯度反固定。虽然体积锁定是一个众所周知的问题，可以在许多不同的离散化方法中解决，但线性弹性的梯度合作感的概念是新的。我们讨论了这两个方面，并提出了新型混合不连续的Galerkin（HDG）方法，以实现线性弹性。这些方法的起点是差异构成离散化。由于其行为良好的stokes限制了该方法是梯度的且无体积锁定的方法。为了提高计算效率，我们还考虑具有放松的差异符合性和修改的离散化，从而使梯度稳定性重新稳定，从而在HDG SuperConvergence的意义上也产生了强大而准确的离散化。
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.
