Consider the following boundary value problem:
$u^{(4)}(x)=x$, $x\in (0,1)$,
$u(0)=u^′(0)=u(1)=u^′(1)=0$,
I want to solve this problem with the finite element method. But given the weak form of the equation in which the second-order derivative exists, I cannot use the basic functions of the first order. I want to know how this problem is solved in finite element method. Please guide me.