Geodesic
A finite element method for solving singular boundary-value problems
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XX, Tome 346 (2007), pp. 149-159

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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. 
@article{ZNSL_2007_346_a10,
     author = {M. N. Yakovlev},
     title = {A finite element method for solving singular boundary-value problems},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {149--159},
     publisher = {mathdoc},
     volume = {346},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2007_346_a10/}
}
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M. N. Yakovlev. A finite element method for solving singular boundary-value problems. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XX, Tome 346 (2007), pp. 149-159. http://geodesic.mathdoc.fr/item/ZNSL_2007_346_a10/