A Posteriori Error Estimates for Approximate Solutions to the Obstacle Problem for the -Laplacian

Abstract: The paper is concerned with a functional identity and estimates that are fulfilled for themeasures of deviations from exact solutions of the obstacle problem for the -Laplacian. They hold true for any functions fromthe corresponding (energy) functional class, which contains the generalized solution to the problemas well. We do not use any special properties of approximations or numerical methods norinformation on the exact configuration of the coincidence set. The right-hand side of the identitiesand estimates contains only known functions and can be explicitly calculated, and the left-handside represents a certain measure of the deviation of the approximate solution from the exact one.The right-hand side of the identity and estimates contains only known functions and can beexplicitly calculated, while and the left-hand side represents a certain measure of the deviation ofthe approximate solution from the exact one. The obtained functional relations allow one toestimate the error of any approximate solutions to the problem regardless of the method of howthey are obtained. In addition, they enable one to compare the exact solutions to problems withdifferent data. The latter provides the possibility to estimate the errors of mathematical models. © 2025 Elsevier B.V., All rights reserved.