Computing eigenvalues and eigenfunctions of the Laplacian for convex polygons
type: Item
instance of: scholarly article
title: Computing eigenvalues and eigenfunctions of the Laplacian for convex polygons
zbMATH Open document ID: 1380.65351
author: Matthew J. Colbrook
author: A. S. Fokas
published in: Applied Numerical Mathematics
publication date: 2018-01-12T00:00:00Z
Mathematics Subject Classification ID: 65N25
Mathematics Subject Classification ID: 35P15
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 65N35
Mathematics Subject Classification ID: 35J05
zbMATH DE Number: 6825874
zbMATH Keywords: elliptic PDEs
zbMATH Keywords: eigenvalues and eigenfunctions
zbMATH Keywords: boundary value problems
zbMATH Keywords: spectral convergence
zbMATH Keywords: unified transform method
zbMATH Keywords: Fokas method
zbMATH Keywords: collocation method
zbMATH Keywords: Helmholtz equation
zbMATH Keywords: Laplacian
describes a project that uses: BEMLIB
MaRDI profile type: Publication
full work available at URL: j.apnum.2017.12.001
OpenAlex ID: W2774884604
cites work: On the rigorous foundations of the Fokas method for linear elliptic partial differential equations
cites work: The Spectral Dirichlet--Neumann Map for Laplace's Equation in a Convex Polygon
cites work: Elliptic PDEs with constant coefficients on convex polyhedra via the unified method
cites work: Laplace's equation on convex polyhedra via the unified method
cites work: The fundamental \(k\)-form and global relations
cites work: Numerical analysis of Fokas' unified method for linear elliptic PDEs
cites work: Optimal estimates for lower and upper bounds of approximation errors in the \(p\)-version of the finite element method in two dimensions
cites work: Q3126801
cites work: Finite element approximation of eigenvalue problems
cites work: Approximation Results for Orthogonal Polynomials in Sobolev Spaces
cites work: Integral Equation Methods in Scattering Theory
cites work: Construction of Corner Singularities for Agmon-Douglis-Nirenberg Elliptic Systems
cites work: A spectrally accurate numerical implementation of the Fokas transform method for Helmholtz-type PDEs
cites work: A unified transform method for solving linear and certain nonlinear PDEs
cites work: On the integrability of linear and nonlinear partial differential equations
cites work: Two-dimensional linear partial differential equations in a convex polygon
cites work: A Unified Approach to Boundary Value Problems
cites work: A semi-analytical numerical method for solving evolution and elliptic partial differential equations
cites work: Eigenvalues for the Laplace operator in the interior of an equilateral triangle
cites work: A numerical implementation of Fokas boundary integral approach: Laplace's equation on a polygonal domain
cites work: An analytical method for linear elliptic PDEs and its numerical implementation
cites work: Isospectral plane domains and surfaces via Riemannian orbifolds
cites work: Q4023365
cites work: Q3093929
cites work: A numerical technique for linear elliptic partial differential equations in polygonal domains
cites work: Linear Elliptic PDEs in a Cylindrical Domain with a Polygonal Cross‐Section
cites work: Can One Hear the Shape of a Drum?
cites work: Numerical quadratures for singular and hypersingular integrals
cites work: Eigenvalues of the Laplacian in Two Dimensions
cites work: Q3270785
cites work: Q4953888
cites work: Q4789271
cites work: Data analysis and representation on a general domain using eigenfunctions of Laplacian
cites work: Efficient numerical solution of the generalized Dirichlet-Neumann map for linear elliptic PDEs in regular polygon domains
cites work: The generalized Dirichlet-Neumann map for linear elliptic PDEs and its numerical implementation
cites work: Direct and iterative solution of the generalized Dirichlet-Neumann map for elliptic PDEs on square domains
cites work: Direct Gauss quadrature formulae for logarithmic singularities on isoparametric elements
cites work: A spectral collocation method for the Laplace and modified Helmholtz equations in a convex polygon
cites work: Q3416799
cites work: Inversion of block-circulant matrices and circular array approach
cites work: On the convergence rates of Legendre approximation
cites work: Mixed boundary value problems in plane domains with corners
DOI: 10.1016/J.APNUM.2017.12.001
description: scientific article; zbMATH DE number 6825874