Geodesic
High-order accuracy approximation for the two-point boundary value problem of the fourth order with degenerate coefficients
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 159 (2017) no. 4, pp. 493-508 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper deals with the construction of high-order accuracy finite element schemes for the fourth-order ordinary differential equation with degenerate coefficients on the boundary. The method for solving the problem is based on both multiplicative and additive-multiplicative separation of singularities. For the given class of smoothness of the right-hand sides, the optimal convergence rate has been proved.
Keywords: two-point boundary value problem, finite element schemes, weight function space, multiplicative and additive-multiplicative decomposition of singularity. 
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     title = {High-order accuracy approximation for the two-point boundary value problem of the fourth order with degenerate coefficients},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
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     year = {2017},
     volume = {159},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2017_159_4_a5/}
}
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A. A. Sobolev; M. R. Timerbaev. High-order accuracy approximation for the two-point boundary value problem of the fourth order with degenerate coefficients. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 159 (2017) no. 4, pp. 493-508. http://geodesic.mathdoc.fr/item/UZKU_2017_159_4_a5/

[1] Tayupov Sh. I., Timerbaev M. R., “Finite element schemes of a high accuracy order for two-pointed heterogenous boundary-value problem with designation”, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 148, no. 4, 2006, 63–75 (In Russian) | Zbl

[2] Sobolev A. A., Timerbaev M. R., “On finite element method of high-order accuracy for two-point degenerated Dirichlet problem of 4th order”, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 152, no. 1, 2010, 235–244 (In Russian) | MR | Zbl

[3] Timerbaev M. R., “Multiplicative extraction of singularities in FEM solvers for degenerate elliptic equations”, Differ. Equations, 36:7 (2000), 1086–1093 | DOI | MR | Zbl

[4] Kudryavtsev L. D., “On equivalent norms in weighted spaces”, Proc. Steklov Inst. Math., 170, 1984, 185–218 (In Russian) | MR | Zbl | Zbl

[5] Nikol'skii S. M., Approximation of Functions of Several Variables and Imbedding Theorems, Nauka, Moscow, 1977, 456 pp. (In Russian) | MR

[6] Triebel H., Interpolation Theory, Function Spaces, Differential Operators, Elsevier Sci. Publ., 1978, 500 pp. | MR | MR

[7] Timerbayev M. R., “Weighted estimates of solution of the Dirichlet problem with anisotropic degeneration on a part of boundary”, Russ. Math., 47:1 (2003), 58–71 | MR | Zbl

[8] Timerbaev M. R., “On FEM schemes for two-point boundary-value Dirichlet problems of the fourth order with weak degeneration”, Issled. Prikl. Mat. Inf., 25, 2004, 78–85 (In Russian)

[9] Ciarlet P., The Finite Element Method for Elliptic Problems, North Holland, 1978, 529 pp. | MR | MR | Zbl