Eigenvalues and eigenfunctions of the Laplace operator on an equilateral triangle for the discrete case.
type: Item
instance of: scholarly article
title: Eigenvalues and eigenfunctions of the Laplace operator on an equilateral triangle for the discrete case.
zbMATH Open document ID: 1059.65101
DOI: 10.1023/A:1013744008028
author: Milan Prager
published in: Applications of Mathematics
publication date: 2005-04-19T00:00:00Z
full work available at URL: https://eudml.org/doc/33085
review text: The author gives explicit formulas for eigenvalues and a complete orthogonal system of eigenvectors of a discretized boundary value problem for the Laplace equation with either Dirichlet or Neumann boundary conditions on an equilateral triangle with a triangular mesh. The technique is analogous to the author's previous paper [ibid. 43, No. 4, 311--320 (1998; Zbl 0940.35059)] in which it was calculated for the continuous case. It is shown that the eigenvalues from the discrete case converge to the ones in the continuous case when the mesh is refined. The problem is transformed to a rectangle and explicit formulas for all eigenvalues and eigenvectors are given.
Mathematics Subject Classification ID: 65N25
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 65N06
Mathematics Subject Classification ID: 35P10
zbMATH DE Number: 2158708
zbMATH Keywords: discrete Laplace operator
zbMATH Keywords: discrete boundary value problem
zbMATH Keywords: eigenvalue
zbMATH Keywords: eigenvector
MaRDI profile type: Publication
cites work: Eigenvalues and eigenfunctions of the Laplace operator on an equilateral triangle
OpenAlex ID: W1570478543
description: scientific article; zbMATH DE number 2158708