The Morley-Type Virtual Element for Plate Bending Problems

Abstract

We propose a simple nonconforming virtual element for plate bending problems, which has few local degrees of freedom and provides the optimal convergence in $$H^2$$ -norm. Moreover, we prove the optimal error estimates in $$H^1$$ - and $$L^2$$ -norm. The nonconforming virtual element is constructed for any order of accuracy, but not $$C^0$$ -continuous. It is worth mentioning that, for the lowest-order case on triangular meshes the simplified nonconforming virtual element coincides with the well-known Morley element, so it can be taken as the extension of the Morley element to polygonal meshes. Finally, we verify the optimal convergence in $$H^2$$ -norm for the nonconforming virtual element by some numerical tests.