弹性问题的一种间断Galerkin有限元法分析(英文)

Analysis of a discontinuous Galerkin method for elasticity problems

作者就弹性问题对应力-位移格式给出了一种间断Galerkin有限元方法,并从理论上分析了该方法能避免locking现象,具有一致稳定性及最优误差估计.此外,利用本文方法的特殊结构,作者由位移的离散解后期导出了一个新的位移近似解,并证明了此解属于H(div,Ω)空间,且在保持同样精度的同时还具守恒性质.

The authors introduce and analyze a discontinuous Galerkin method for linear elasticity only based on the displacement-stress formulation. It＇s locking-free, uniformly stable and possesses optimal error estimate. Then a simple post-processing is introduced which takes advantage of the special structure of the method. It allows us to construct an post-processed displacement from the discrete one. The new approximation to the displacement is H（div,Ω）-conforming and keeps the same accuracy. In particular, it ensures the conservation laws element-by-element.