Geodesic
Refined-mesh interpolation method for functions with a boundary-layer component
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 9, pp. 1673-1684

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Linear and quadratic spline interpolation methods for a one-variable function with a boundary-layer component are examined. It is shown that the interpolation method for such a function leads to considerable errors when applied on a uniform mesh. The error of linear and quadratic spline interpolations on meshes that are refined in the boundary layer is estimated. Numerical results are presented. 
@article{ZVMMF_2008_48_9_a11,
     author = {A. I. Zadorin},
     title = {Refined-mesh interpolation method for functions with a~boundary-layer component},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1673--1684},
     publisher = {mathdoc},
     volume = {48},
     number = {9},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_9_a11/}
}
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A. I. Zadorin. Refined-mesh interpolation method for functions with a boundary-layer component. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 9, pp. 1673-1684. http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_9_a11/