Wouldn't it work to just to this:

v = v + (h/2.0*vnorm)*dot(velocity, grad(v))
U = 0.5*(u0 + u)
F = v*(u - u0)*dx + 0.5*k*(v*dot(velocity, grad(U))*dx + c*dot(grad(v), 
grad(U))*dx) - k*v*f*dx
a = lhs(F)
L = rhs(F)

That's my understanding of SUPG, but perhaps I've missed something?

--
Anders

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