Discretization of solutions of Poisson equation by inaccurate information

Abstract

Partial differential equations, along with the function, derivative, and integral, are among the basic mathematical models. Their solutions, even when expressed explicitly through series or integrals, are in fact again inaccessible to direct computer calculations infinite objects. Therefore, the problem of approximating them with finite objects arises, the mathematical formulation of which is contained in the definition of the Computational (numerical) diameter.

In the article the problem of discretization by inaccurate information of solutions of Poisson equations with right-hand side $f$  belongs to the anisotropic Korobov classes $E^{r_1,...,r_s}$  is considered. There are obtained upper bound of error of discretization by innacurate information from values at point of $f$  in uniform metric. Wherein, the boundaries of inaccurate information which keep the order of discretization by accurate information are obtained. Computational aggregates constructed by optimal Korobov quadrature formulas with equal weights and nodes, which found by algorithms based on divisor theory.