A Virtual Element Numerical Approximation for the Vibration Problem of a Thin Plate

We focus our attention in the development of a virtual element method for the approximation of the vibration problem of a thin plate modeled by Kirchhoff-Love equations. We introduce a weak variational formulation based on the Sobolev space H2. In addition, we propose a discretization by means of the lowest-order non conforming elements. We show that the resulting scheme provides a correct approximation of the spectrum and prove optimal-order error estimates. Finally, we report some numerical tests supporting our theoretical results.