basically i think i just need to know the method to find the coefficients in a general finite element method, when the problem is given as a weak formulation, using n equally spaced hat functions as a basis...
I have the weak formulation of a boundary value problem a(u,v)=l(v) (attached in picture form)..
How can i construct the finite element approximation to the BVP based on piecewise elements on the subdivision a=X0<X1<...<Xn=b., with uniform spacing h, and show that this gives n+1 equations in n+1 unknowns..