A non‐conforming piecewise quadratic finite element on triangles

It is shown in this paper that non‐conforming finite elements on the triangle using second‐degree polynomials can be easily built and used. Indeed they appear as an ‘enriched’ version of the standard piecewise quadratic six‐node element. This work is divided into two parts. In the first we present the basic properties of the element, namely how it can be built and basic error estimates. We also show that this element exhibits a very peculiar regularity property. In the second part we apply our element to the approximation of viscous incompressible flows and more generally to the approximation of incompressible materials.