Discretization of Solutions of the Poisson Equation on the Anisotropic Sobolev Class

A. B. Utesov, A. A. Bazarkhanova

2026

Data confidence 70 medium

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Abstract

Abstract A discretization operator for the solution of the Poisson equation with right-hand side in an anisotropic Sobolev class is constructed based on the values of this function at the points of a grid uniform along each axis. We obtain an upper bound for the discretization error of the solution in the Hilbert metric and prove that this bound is order sharp. This estimate, unlike the well-known order-sharp estimates obtained when considering the Korobov class and the isotropic Sobolev class, is independent of the dimension of the anisotropic Sobolev class.