How to create a nodal basis of an enriched FEM or how to create my own FEM?

Hi,

I would like to implement the mass-lumping algorithm for the higher order FEM according to the ideas presented in "Higher order triangular finite elements with mass lumping for the wave equation", G. Cohen, P. Joly, J. E. Roberts and N. Tordjman, SIAM J. NUMER. ANAL., Vol. 38, No. 6, pp. 2047–2078.

This requires the use of either standard $P_2$ (piecewise quadratic) or $P_3$ (piecewise cubic) elements, which are additionaly enriched by bubble functions. However, it is crucial to use a nodal basis in the enriched space to obtain the mass-lumping. This is not done by default when one uses

G = FunctionSpace(mesh, "CG", 2)
B = FunctionSpace(mesh, "Bubble", 3)
V = G + B

Is it then possible to define a nodal basis in this enriched space?

Would it be maybe easier to define a new finite element space (equal to the enriched space) spanned by a desired nodal basis? If yes, then how can this be done?

Thanks in advance!