Geodesic
On finite element method of high-order accuracy for two-point degenerated Dirichlet problem of 4th order
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 152 (2010) no. 1, pp. 235-244

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In this paper two-point boundary value problem for a differential equation of 4th order with degeneration is considered. This problem is solved by the finite element method of high-order accuracy with a multiplicative separation of singularity. The optimal convergence rate of the presented method for a given class of smoothness of the right-hand sides is proved.
Keywords: two-point boundary value problem, weighted Sobolev space, finite element method, multiplicative decomposition of singularity. 
@article{UZKU_2010_152_1_a21,
     author = {A. A. Sobolev and M. R. Timerbaev},
     title = {On finite element method of high-order accuracy for two-point degenerated {Dirichlet} problem of 4th order},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {235--244},
     publisher = {mathdoc},
     volume = {152},
     number = {1},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2010_152_1_a21/}
}
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A. A. Sobolev; M. R. Timerbaev. On finite element method of high-order accuracy for two-point degenerated Dirichlet problem of 4th order. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 152 (2010) no. 1, pp. 235-244. http://geodesic.mathdoc.fr/item/UZKU_2010_152_1_a21/