论文标题
应变梯度弹性模型的强大下阶混合有限元法
A robust lower order mixed finite element method for a strain gradient elasticity model
论文作者
论文摘要
为应变梯度弹性（SGE）模型开发了强大的不合格混合有限元方法。在两个和三个维度的情况下，低阶$ c^0 $ - 连续$ h^2 $ -NONCON-NONCON-NONCON-NONCONTINE元素是通过用泡泡函数丰富的二次拉格朗日元素来为位移字段构建的。利用这将与线性拉格朗日元素一起离散为SGE模型的混合配方。建立了强大的离散INF-SUP条件。相对于小尺寸参数和拉梅系数的尖锐而均匀的误差估计，也可以通过数值结果来验证。另外，在两个合理的假设下得出了SGE模型的均匀规律性。
A robust nonconforming mixed finite element method is developed for a strain gradient elasticity (SGE) model. In two and three dimensional cases, a lower order $C^0$-continuous $H^2$-nonconforming finite element is constructed for the displacement field through enriching the quadratic Lagrange element with bubble functions. This together with the linear Lagrange element is exploited to discretize a mixed formulation of the SGE model. The robust discrete inf-sup condition is established. The sharp and uniform error estimates with respect to both the small size parameter and the Lamé coefficient are achieved, which is also verified by numerical results. In addition, the uniform regularity of the SGE model is derived under two reasonable assumptions.
