A three-dimensional quadratic nonconforming element (Q1065497)

A second-degree nonconforming element on tetrahedra generalizing the construction of the 2-D nonconforming quadratic element (on triangle) is defined. Properties of this new element are studied, and a basis for the approximation space derived from this element is built. A discrete regularity property is demonstrated similar to the one that holds for the corresponding two-dimensional element. The work gives important explanations about the non-conforming 3-D elements.