A C0 Interior Penalty Finite Element Method for Flexoelectricity

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 simplified case. Standard high-order finite element approximations, nodal basis, are considered. The proposed C0-IPM formulation involves second derivatives in elements, plus integrals on mesh faces (sides 2D), that impose {C}}^1$$ continuity displacement weak form. is stable large enough parameter, which can be estimated solving an eigenvalue problem. applicability and convergence demonstrated 2D 3D numerical examples.