A new class of nonconforming finite elements for the enrichment of Q1 element on convex polytope

This paper establishes a new class of nonconforming finite elements by including additional enriched functions (not necessary polynomials) to the standard Q1(K)Q1(K) element on convex polytope. Here we focus on their fundamental construction principles and some of their approximation properties. In addition, we show how this approach can be used to enrich locally the well-known Wilson element. The present enrichment method for this class of Wilson-type nonconforming finite element is based on a single univariate function, and some arbitrary number of free parameters. We also obtain explicit expressions for the basis functions of the new enriched element.