Serendipity Nodal VEM spaces

Abstract We introduce a new variant of Nodal Virtual Element spaces that mimics the "Serendipity Finite Element Methods" (whose most popular example is the 8-node quadrilateral) and allows to reduce (often in a significant way) the number of internal degrees of freedom. When applied to the faces of a three-dimensional decomposition, this allows a reduction in the number of face degrees of freedom: an improvement that cannot be achieved by a sim- Finite Elements, but are much more robust with respect to element distortions. On more general polytopes the Serendipity VEMs are the natural (and simple) generalization of the simplicial case