An adaptive approach to solutions of Fredholm integral equations of the second kind
type: Item
instance of: scholarly article
title: An adaptive approach to solutions of Fredholm integral equations of the second kind
zbMATH Open document ID: 1474.65499
DOI: 10.1155/2014/629179
author: Nebiye Korkmaz
author: Zekeriya Güney
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: As an approach to approximate solutions of Fredholm integral equations of the second kind, adaptive hp-refinement is used firstly together with Galerkin method and with Sloan iteration method which is applied to Galerkin method solution. The linear hat functions and modified integrated Legendre polynomials are used as basis functions for the approximations. The most appropriate refinement is determined by an optimization problem given by \textit{L. F. Demkowicz} [Computing with \(hp\)-adaptive finite elements. Vol. 1: One- and two-dimensional elliptic and Maxwell problems. Boca Raton, FL: Chapman \& Hall/CRC (2007; Zbl 1111.65103)]. During the calculations \(L^2\)-projections of approximate solutions on four different meshes which could occur between coarse mesh and fine mesh are calculated. Depending on the error values, these procedures could be repeated consecutively or different meshes could be used in order to decrease the error values.
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45B05
zbMATH DE Number: 7022770
Wikidata QID: Q59040166
describes a project that uses: Vascular Modeling Toolkit
describes a project that uses: Algorithm 876
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/629179
OpenAlex ID: W2016990490
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description: scientific article; zbMATH DE number 7022770