Abstract
A discretization operator for the solution of the Poisson equation with the right-hand sidefrom the Korobov class is constructed and its error is estimated in the \(L^{p}\) -metric, \(2\leq p\leq \infty\) . It is proved that for \(p=2\) the resulting error estimate for the discretizationoperator is order sharp on the power scale. An error in calculating the trigonometric Fouriercoefficients used when constructing the discretization operator is also found. It should be notedthat the obtained estimate in one case is better than previously known estimates of the errors ofdiscretization operators constructed from the values of the right-hand side of the equation at thenodes of the modified Korobov grid and the Smolyak grid, and in the other case it coincides withthem up to constants.
