Combined Legendre Spectral-Finite Element Methods for Two-Dimensional Fredholm Integral Equations of the Second Kind. (22nd November 2022)

• Record Type: Journal Article
• Authors: Panigrahi, Bijaya Laxmi
• Is Part Of: Numerical functional analysis and optimization. Volume 43:Number 16(2022)
• Page Start: 1801
• Page End: 1820
• Publication Date: 2022-11-22
• Subjects: Combined Legendre spectral-finite element methods -- eigenvalue problem -- finite element method -- Fredholm integral equations -- Legendre spectral method; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2022.2135540
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: In this paper, we will discuss on the Combined Legendre spectral-Finite element methods (CLSFEM) for the two-dimensional Fredholm integral equations with smooth kernel on the Banach spaces and the corresponding eigenvalue problem. In these methods, the approximated finite dimensional space is the cartesian product of spline space and Legendre polynomial space. The problem is approximated by the CLSFEM using orthogonal projection, which projects from the Banach space into the finite dimensional space. The convergence analysis for both Fredholm integral equations and the corresponding eigenvalue problem will be discussed in both L 2 and L ∞ norms. The numerical results will be shown to validate the theoretical estimate.