By using the Legendre-Gauss-Lobatto (LGL) quadrature formula (QF) and LGL nodal points one achives a diagonal mass-matrix for finite element problems. (More specifically, the spectral element method.)
Setting the $n$ quadrature points as nodal points, the polynomials of the ansatz and test space are of degree $n-1$.
The LGL QF is exact up to degree $2n-3$, but the mass-matrix should contain integrals of polynomials with degree $2n-2$.
Is it normal for this kind of method, that each integral is inexact?
Is it possible at all to combine a DG-method with this ansatz of the spectral element method (SEM)?
Any tips, pointers and literature will be appreciated.