3. (60 points) Consider our familiar second order strong form:
\frac{d}{dx} \left( a(x) \frac{du}{dx} \right) + c(x)u = f(x), for 0 < x < 2h
We seek a 3-node, two element finite element solution using linear Lagrange interpolation func-
tions and the discretization as shown below:
1
element 1
2
element 2
3
x=0
x=h
x=2h
If the given problem data is:
h = 1, a(x) = 1, c(x) = 0, f(x) = 2h - x
with boundary conditions
u(x = 0) = 0, u(x = 2h) = 4
compute $U_2$ and u(x = 1.35h). i.e., compute the unknown u at node-2 and also at the location
specified by x = 1.35h.
