# Galerkin Method

Can someone please explain this to me, the part where we take the integrals, why is it not $\frac{1}{ \Delta x^{2}}$ for K11 how do they get 2\deltax >?

The basis functions are supported on very small intervals, so while both of them contribute a $\frac{1}{\Delta x}$, the length of the interval is only $\Delta x$ so we end up with an interval on the order of $$\frac{1}{\Delta x^2} \Delta x = \frac{1}{\Delta x}$$
• You can explicitly do the integrals to see exactly where everything comes from. The actual support of each basis function has length $2\Delta x$ which is why there is a two. The support of adjacent functions overlap on intervals of length $\Delta x$. – User8128 May 19 '17 at 23:03