Geodesic
Cubature formulas for a two-variable function with boundary-layer components
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 12, pp. 1997-2007 
A. I. Zadorin. Cubature formulas for a two-variable function with boundary-layer components. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 12, pp. 1997-2007. http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_12_a4/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Cubature formulas for evaluating the double integral of a two-variable function with boundary-layer components are constructed and studied. Because of the boundary-layer components, the cubature formulas based on Newton–Cotes formulas become considerably less accurate. Analogues of the trapezoidal and Simpson rules that are exact for the boundary-layer components are constructed. Error estimates for the constructed formulas are derived that are uniform in the gradients of the integrand in the boundary layers.

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