A finite element method for solving singular boundary-value problems

It is proved that under certain assumptions on the functions $q(t)$ and $f(t)$, there is one and only one function $u_0(t)\in\overset{o}W{}^1_2(a,b)$ at which the functional
$$ \int^b_a[u'(t)]^2 dt+\int^b_a q(t)u^2(t)dt-2\int^b_a f(t)u(t)dt $$
attains its minimum. An error bound for the finite element method for computing the function $u_0(t)$ in terms of $q(t)$, $f(t)$, and the meshsize $h$ is presented.