A POSTERIORI ERROR ESTIMATES FOR APPROXIMATE SOLUTIONS OF THE OBSTACLE PROBLEM FOR THE 𝑝-LAPLACIAN

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Abstract

The paper is concerned with a functional identity and estimates which are fulfilled for the measures of deviations from exact solutions of the obstacle problem for the 𝑝-Laplacian. They hold true for any functions from the corresponding (energy) functional class, which contains the generalised solution of the problem as well. We do not use any special properties of approximations or numerical methods nor information of the exact configuration of the coincidence set. The right-hand side of the identities and estimates contains only known functions and can be explicitly calculated, and the left side represents a certain measure of the deviation of the approximate solution from the exact solution. The right-hand side of the identity and estimates contains only known functions and can be explicitly calculated, while and the left side represents a certain measure of the deviation of the approximate solution from the exact one. The obtained functional relations allow to estimate the error of of any approximate solutions of the problem regardless of the method of their obtaining. In addition, they enable to compare the exact solutions of problems with different data. The latter provides the possibility to estimate the errors of mathematical models.

About the authors

D. E Apushkinskaya

People’s Friendship University of Russia named after Patrice Lumumba

Email: apushkinskaya@gmail.com
Moscow, Russia

A. A Novikova

People’s Friendship University of Russia named after Patrice Lumumba

Email: aanovikova01@gmail.com
Moscow, Russia

S. I Repin

People’s Friendship University of Russia named after Patrice Lumumba; Saint Petersburg Department of Steklov Mathematical Institute of RAS

Email: rpnspb@gmail.com
Moscow, Russia

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