Geodesic
About the uniform convergence of parabolic spline interpolation on the class of functions with large gradients in the boundary layer
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 20 (2017) no. 2, pp. 131-144

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A problem of the Subbotin parabolic spline-interpolation of functions with large gradients in the boundary layer is considered. In the case of a uniform grid it has been proved and in the case of the Shishkin grid it has been experimentally shown that with a parabolic spline-interpolation of functions with large gradients the error in the exponential boundary layer can unrestrictedly increase with a fixed number of grid nodes. A modified parabolic spline has been constructed. Estimates of the interpolation error of the constructed spline don't depend from a small parameter. 
@article{SJVM_2017_20_2_a1,
     author = {I. A. Blatov and A. I. Zadorin and E. V. Kitaeva},
     title = {About the uniform convergence of parabolic spline interpolation on the class of functions with large gradients in the boundary layer},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {131--144},
     publisher = {mathdoc},
     volume = {20},
     number = {2},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2017_20_2_a1/}
}
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I. A. Blatov; A. I. Zadorin; E. V. Kitaeva. About the uniform convergence of parabolic spline interpolation on the class of functions with large gradients in the boundary layer. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 20 (2017) no. 2, pp. 131-144. http://geodesic.mathdoc.fr/item/SJVM_2017_20_2_a1/