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.

我们提出了一种\({\mathcal {C}}^0\)内部惩罚方法 (C0-IPM) 用于挠曲电的计算建模，作为一个简化的例子，它也适用于应变梯度弹性。考虑了具有节点基础的标准高阶\({\mathcal {C}}^0\)有限元近似值。提议的 C0-IPM 公式涉及单元内部的二阶导数，加上网格面（2D 中的边）上的积分，以弱形式强加\({\mathcal {C}}^1\)位移的连续性. 对于足够大的内部惩罚参数，该公式是稳定的，可以估计解决特征值问题。通过 2D 和 3D 数值例子证明了该方法的适用性和收敛性。