I have a finite element theory question (so likely for @tjhei or @bangerth, but anyone with FE experience is welcome to chime in):
By default we often use a Gauss quadrature with
FE_degree+1 for our assemblers, because that can accurately integrate polynomials of order
2*n-1 = 2*FE_degree+1, and can therefore accurately represent terms like
phi_u * phi_u, which is of polynomial degree 2 * FE_degree. However we often use the same quadrature degrees in our postprocessors, where we simply want to integrate over the solution vector, which is of degree
FE_degree. If I am not mistake in order to integrate this accurately we would only need a Gauss quadrature of order
FE_degree/2 + 1. Is this correct? Because then we can reduce the quadrature order in many postprocessors (I am particularly looking at the depth average, because it is so expensive, and @maxrudolph needs it frequently in his models, every reduction in quadrature order would make it significantly cheaper).
Any advice is appreciated.