The problem definition in G. Sadaka's Wave Equation example

G. Sadaka provide an examplein solving Wave Equation. Math equation is:

The problem definition in Sadaka’s code is:

problem tambour(uh,vh) = int2d(Th)(uh*vh + Grad(uh)'*Grad(vh)*(c*dt)^2*.5 )
					+ int2d(Th)(Grad(uh0)'*Grad(vh)*(c*dt)^2*.5 ) 
					- int2d(Th)(2.*uh1*vh - uh0*vh)
					+ on(1,2,3,4,uh=0.);

I want to know why there is a int2d(Th)(Grad(uh0)'*Grad(vh)*(c*dt)^2*.5 ) term (the 2nd row). If we approximate u_tt with (u-2*u_{t-1}+u_{t-2})/(dt)^2 and set u_{t-1} to uh1, u_{t-2} to uh0, then we can get the 1st and 3rd row but not the 2nd.

Finally I find that Sadaka use (\Delta u+\Delta u_{t-1})/2 to approximate \Delta u,so there is a .5 in the problem.