Please use this identifier to cite or link to this item: https://hdl.handle.net/20.500.11851/7398
Title: RESULTS ON NONLOCAL BOUNDARY VALUE PROBLEMS
Authors: Aksoylu, Burak
Mengesha, Tadele
Keywords: Condition number
Nonlocal boundary value problems
Nonlocal operators
Nonlocal Poincare inequality
Peridynamics
Preconditioning
Well-posedness
Issue Date: 2010
Publisher: Taylor & Francis Inc
Abstract: In this article, we provide a variational theory for nonlocal problems where nonlocality arises due to the interaction in a given horizon. With this theory, we prove well-posedness results for the weak formulation of nonlocal boundary value problems with Dirichlet, Neumann, and mixed boundary conditions for a class of kernel functions. The motivating application for nonlocal boundary value problems is the scalar stationary peridynamics equation of motion. The well-posedness results support practical kernel functions used in the peridynamics setting. We also prove a spectral equivalence estimate which leads to a mesh size independent upper bound for the condition number of an underlying discretized operator. This is a fundamental conditioning result that would guide preconditioner construction for nonlocal problems. The estimate is a consequence of a nonlocal Poincare-type inequality that reveals a horizon size quantification. We provide an example that establishes the sharpness of the upper bound in the spectral equivalence.
URI: https://doi.org/10.1080/01630563.2010.519136
https://hdl.handle.net/20.500.11851/7398
ISSN: 0163-0563
Appears in Collections:Matematik Bölümü / Department of Mathematics
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

Show full item record

CORE Recommender

SCOPUSTM   
Citations

52
checked on Sep 23, 2022

WEB OF SCIENCETM
Citations

51
checked on Sep 24, 2022

Page view(s)

4
checked on Dec 26, 2022

Google ScholarTM

Check

Altmetric


Items in GCRIS Repository are protected by copyright, with all rights reserved, unless otherwise indicated.