Two robust nonconforming H${}^2-$elements for linear strain gradient elasticity

We propose two nonconforming finite elements to approximate a boundary value problem arising from strain gradient elasticity, which is a higher-order perturbation of the linearized elastic system. Our elements are H${}^2-$nonconforming while H${}^1-$conforming. We show both elements converges in the energy norm uniformly with respect to the perturbation parameter.