论文标题
C0内部惩罚有限元法的灵活性元素方法
A C0 interior penalty finite element method for flexoelectricity
论文作者
论文摘要
我们建议使用$ \ Mathcal {C}^0 $内部惩罚方法（C0-IPM），用于柔韧性的计算建模，并应用于简化的情况，并应用于应变梯度弹性。考虑了标准的高阶$ \ Mathcal {C}^0 $有限元近似值，具有节点为基础。所提出的C0-IPM公式涉及元素内部的第二个衍生物，以及网格面上的积分（2D的侧面），它们以弱形式施加了$ \ Mathcal {C}^1 $连续性。该公式对于足够大的内部惩罚参数是稳定的，可以估计解决特征值问题。用2D和3D数值示例证明了该方法的适用性和收敛性。
We propose a $\mathcal{C}^0$ Interior Penalty Method (C0-IPM) for the computational modelling of flexoelectricity, with application also to strain gradient elasticity, as a simplified case. Standard high-order $\mathcal{C}^0$ finite element approximations, with nodal basis, are considered. The proposed C0-IPM formulation involves second derivatives in the interior of the elements, plus integrals on the mesh faces (sides in 2D), that impose $\mathcal{C}^1$ continuity of the displacement in weak form. The formulation is stable for large enough interior penalty parameter, which can be estimated solving an eigenvalue problem. The applicability and convergence of the method is demonstrated with 2D and 3D numerical examples.
