Nodal and Mixed Bases

 We have so far presented a hybrid basis derived from Dubiner's [16] C⁰ basis for the triangle. This dictates the shapes of the edge and vertex modes for the quadrilateral. We will now consider an alternative starting point. In the spectral element method [7], quadrilateral elements are commonly used with a nodal basis, constructed from the Legendre interpolant polynomials. This method benefits from a fast transform to the polynomial space, due to the collocation property of the modes. Similarly, inner products can be evaluated efficiently.