Quadrilateral Basis: ${\bf QuNN}$

This basis is constructed based on the Gauss-Lobatto-Legendre interpolant of order N already defined as $\{h_n(r)\}$. It was first used for spectral element discretizations in [33]. This is a nodal non-hierarchical basis.

For consistency we present the ${\bf QuNN}$basis in the same format as the hierarchical basis:

Vertex Modes:

Edge Modes (1 < n, m < N):

Interior Modes ( 1 < n, m < N ):

We represent this basis for N=5 in figure 3.7; all modes are fourth degree polynomials.

  

Figure 3.7: Mode shapes for the quadrilateral nodal basis (${\bf QuNN}$) with N=5.