Geodesic
Discretization of solutions to Poisson’s equation in the Korobov class
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 7, pp. 1082-1093

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A sharp discretization error estimate on the power scale is obtained for the solution of Poisson’s equation with a right-hand side from the Korobov class with the application of Smolyak grid nodes. In some cases, the results coincide in the order of the upper error estimate with earlier results of other authors, but the discretization operator proposed is simpler. 
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     author = {S. S. Kudaibergenov and S. G. Sabitova},
     title = {Discretization of solutions to {Poisson{\textquoteright}s} equation in the {Korobov} class},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
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     publisher = {mathdoc},
     volume = {53},
     number = {7},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_7_a3/}
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S. S. Kudaibergenov; S. G. Sabitova. Discretization of solutions to Poisson’s equation in the Korobov class. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 7, pp. 1082-1093. http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_7_a3/