A multi-scale patch approximation for Poisson problems with a small inhomogeneous inclusion
Year: 2025
Type: article
Abstract: The paper deals with the multi-scale approximation of the influence of a small inhomogeneity of arbitrary shape in an elastic medium. A new multi-scale patch method is introduced, whose caracteristic is to deal with a large scale problem without inclusion, a small-scale problem on a patch surrounding the inclusion defining a corrector and an iterative procedure between these two problems. Theoretical results of convergence of the iterations, a posteriori error estimate and comparison of the corrector with the asymptotic expansion are provided. The finite element approximation is also addressed together with some numerical tests.
DOI: 10.5802/smai-jcm.121
Institutions: Tunis University, National Engineering School of Tunis, ENSIT, Tunis El Manar University, University of Carthage, National Institute of Applied Science and Technology, Lyon 1 Université, École Centrale de Lyon, Centre National de la Recherche Scientifique, Institut Camille Jordan, Université Jean Monnet, Institut National des Sciences Appliquées de Lyon, Université Jean Monnet, Michelin (France), Laboratoire de Mécanique des Contacts et des Structures
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4389904796