How can one correctly represent the nonlinear terms like Hu^2 or q^2/H or q*u in a Discontinuous Galerkin discretization?

Because if I expand the conserved variables namely, the free surface z and the discharge q in series of their various basis functions, then representation of their ratio q/z or product q*z becomes ratio or product of two series which I am not sure is correct. How does one work around this, please?

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