Geodesic
Discretization of the solutions to Poisson's equation
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 9, pp. 1594-1604

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Sharp estimates (in the power scale) are obtained for the discretization error in the solutions to Poisson's equation whose right-hand side belongs to a Korobov class. Compared to the well-known Korobov estimate, the order is almost doubled and has an ultimate value in the power scale. 
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E. A. Bailov; N. Temirgaliev. Discretization of the solutions to Poisson's equation. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 9, pp. 1594-1604. http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_9_a4/