Estimates of the modeling error generated by homogenization of an elliptic boundary value problem

Abstract

In this paper, we derive a posteriori bounds of the di erence between the exact solution of an elliptic boundary value problem with periodic coe cients and an abridged model, which follows from the homogenization theory. The di erence is measured in terms of the energy norm of the basic problem and also in the combined primal–dual norm. Using the technique of functional type a posteriori error estimates, we obtain two-sided bounds of the modeling error, which depends only on known data and the solution of the homogenized problem. It is proved that the majorant with properly chosen arguments possesses the same convergence rate, which was established for the true error. Numerical tests con rm the effi ciency of the estimates.