I have the 1D differential equation $-e^xu'' -e^xu' + u = f(x)$ with BC $u(0)=u(1)=0$ I am trying to come up with the $N\times N$ FEM matrix for this problem.
So first I get the weak formulation of the problem:
$$\int_\Omega -e^xu''\phi_i(x)-e^xu'\phi_i(x)+u\phi_i(x)= \int_\Omega f(x)\phi_i(x)$$
Normally I think you are supposed to use integration by parts to have only terms with a single derivative. But getting the differentiation by parts when I have 3 functions in the product is proving challenging for me.
Is there a different way (computer programs included) where I could get the stiffness matrix for the problem?