Geodesic
Schemes of the finite element method with separation of singularity for a~two-point boundary-value problem of the 4th order with degenerate coefficients
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2011), pp. 88-92.

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In this paper we construct a high accuracy variant of the finite element method for an ordinary differential equation of the fourth order whose coefficients are degenerate on the boundary. The proposed technique is based on the multiplicative and additive-multiplicative separation of singularity. We prove that the convergence rate of the proposed technique is optimal in a given class of smoothness of right-hand sides.
Keywords: two-point boundary value problem, finite element schemes, weight function spaces, multiplicative and additive-multiplicative separation of singularity. 
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     author = {A. A. Sobolev and M. R. Timerbaev},
     title = {Schemes of the finite element method with separation of singularity for a~two-point boundary-value problem of the 4th order with degenerate coefficients},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
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A. A. Sobolev; M. R. Timerbaev. Schemes of the finite element method with separation of singularity for a~two-point boundary-value problem of the 4th order with degenerate coefficients. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2011), pp. 88-92. http://geodesic.mathdoc.fr/item/IVM_2011_5_a12/

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[2] Sobolev A. A., Timerbaev M. R., “O skhemakh MKE vysokogo poryadka tochnosti dlya dvukhtochechnoi zadachi Dirikhle chetvertogo poryadka s vyrozhdeniem”, Uchen. zap. Kazansk. un-ta. Ser. Fiz.-matem. nauki, 152, no. 1, 2010, 235–244

[3] Timerbaev M. R., “Multiplikativnoe vydelenie osobennosti v skhemakh MKE dlya ellipticheskikh vyrozhdayuschikhsya uravnenii”, Differents. uravneniya, 36:7 (2000), 1086–1093 | MR | Zbl