Fulltext

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

Repin, Sergey ; Samrowski, Tatiana ; Sauter, Stefan

In: Journal of Numerical Mathematics, 2016, vol. 24, no. 1, p. 1-15

Ajouter à la liste personnelle
    Titre
    • Estimates of the modeling error generated by homogenization of an elliptic boundary value problem
    Auteur
    • Repin, Sergey. V. A. Steklov Institute of Mathematics, Fontanka 27, 191011 St. Petersburg, Russia, and University of Jyväskylä, Finland
    • Samrowski, Tatiana. Institute for Applied Mathematics and Physics, Zurich University of Applied Sciences, Technikumstrasse 6, CH-8400 Winterthur, Switzerland
    • Sauter, Stefan. Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zurich, Switzerland
    Type de document
    • Postprint
    Langue
    • Anglais
    Publié dans
    • Journal of Numerical Mathematics, 2016, vol. 24, no. 1, p. 1-15. De Gruyter
    Autre version électronique
    Identifiant OAI-PMH
    • oai:doc.rero.ch:324729
    Summary
    In this paper, we derive a posteriori bounds of the difference between the exact solution of an elliptic boundary value problem with periodic coefficients and an abridged model, which follows from the homogenization theory. The difference 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 modelling 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 confirm the efficiency of the estimates.