标题： 有限元空间上的断裂 Hardy 不等式及其在应变梯度弹性中的应用 显示英文标题

标题： A broken Hardy inequality on finite element space and application to strain gradient elasticity

摘要： 我们在不连续有限元空间上展示了断裂的Hardy不等式，其随着网格尺寸的对数因子而爆炸。 这是由自然边界条件下的应变梯度弹性数值分析所引发的。 采用一种混合有限元对来求解该模型，适用于几乎不可压缩材料。 该对具有对数因子的准稳定性，这在近似误差中并不显著，并且在不可压缩极限下稳健收敛，并在微观材料参数中一致收敛。 数值结果支持理论预测几乎是最优的。 此外，在光滑区域上，借助Agmon-Douglis-Nirenberg理论证明了该模型的正则性估计。 显示英文摘要

摘要： We illustrate a broken Hardy inequality on discontinuous finite element spaces, blowing up with a logarithmic factor with respect to the meshes size. This is motivated by numerical analysis for the strain gradient elasticity with natural boundary conditions. A mixed finite element pair is employed to solve this model with nearly incompressible materials. This pair is quasi-stable with a logarithmic factor, which is not significant in the approximation error, and converges robustly in the incompressible limit and uniformly in the microscopic material parameter. Numerical results back up that the theoretical predictions are nearly optimal. Moreover, the regularity estimates for the model over a smooth domain have been proved with the aid of the Agmon-Douglis-Nirenberg theory.