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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     author = {M. N. Yakovlev},
     title = {A finite element method for solving singular boundary-value problems},
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     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/

[1] M. N. Yakovlev, “Razreshimost singulyarnykh kraevykh zadach dlya obyknovennykh differentsialnykh uravnenii poryadka $2m$”, Zap. nauchn. semin. POMI, 309, 2004, 174–188 | MR | Zbl

[2] M. N. Yakovlev, “Suschestvovanie neotritsatelnykh reshenii singulyarnykh kraevykh zadach dlya obyknovennykh differentsialnykh uravnenii vtorogo poryadka”, Zap. nauchn. semin. POMI, 323, 2005, 215–222 | MR | Zbl

[3] M. N. Yakovlev, “Pervaya kraevaya zadacha dlya singulyarnogo nelineinogo obyknovennogo differentsialnogo uravneniya chetvertogo poryadka”, Zap. nauchn. semin. POMI, 334, 2006, 233–245 | MR | Zbl