A quasi-interpolation method for finite element spaces

A combination of Taylor polynomial approximation and averaging results in a powerful quasi-interpolation technique that can be used to analyze the approximation properties of finite element spaces. With this particular approach, the notion of affine equivalent families is completely bypassed in the sense that the degrees of freedom are defined locally rather than being exported from a reference element. In particular, domains with curved boundaries can be handled in a natural manner. Finally, the ease of its application to a particular finite element makes it a valuable pedagogical tool.