Práger, Milan Eigenvalues and eigenfunctions of the Laplace operator on an equilateral triangle for the discrete case. (English) Zbl 1059.65101 Appl. Math., Praha 46, No. 3, 231-239 (2001). 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. Reviewer: Jan Zítko (Praha) Cited in 1 Document MSC: 65N25 Numerical methods for eigenvalue problems for boundary value problems involving PDEs 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation 65N06 Finite difference methods for boundary value problems involving PDEs 35P10 Completeness of eigenfunctions and eigenfunction expansions in context of PDEs Keywords:discrete Laplace operator; discrete boundary value problem; eigenvalue; eigenvector Citations:Zbl 0940.35059 PDF BibTeX XML Cite \textit{M. Práger}, Appl. Math., Praha 46, No. 3, 231--239 (2001; Zbl 1059.65101) Full Text: DOI EuDML OpenURL References: [1] M. Práger: Eigenvalues and eigenfunctions of the Laplace operator on an equilateral triangle. Appl. Math. 43 (1998), 311-320. · Zbl 0940.35059 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.