Short note on the mass matrix for GaussLobatto grid points
The mass matrix for GaussLobatto grid points is usually approximated by GaussLobatto quadrature because this leads to a diagonal matrix that is easy to invert. The exact mass matrix and its inverse are full. We show that the exact mass matrix and  its inverse differ from the approximate diagonal ones by a simple rank-1 update (outer product). They can thus be applied to an arbitrary vector in O(N) O ( N ) operations instead of O(N2) O ( N 2 ) .
mass matrix gausslobatto quadrature spectral methods discontinuous galerkin methods finite element methods