Error analysis of the Trefftz method for solving Laplace's eigenvalue problems

DOI10.1016/j.cam.2005.12.017zbMath1109.65095OpenAlexW1982918936MaRDI QIDQ859885

N. E. Zubov

Publication date: 22 January 2007

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2005.12.017

zbMATH Keywords

numerical experimentserror analysisinterfacesHelmholtz equationboundary approximation methodLaplace eigenvalue

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Error bounds for boundary value problems involving PDEs (65N15) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25)

Related Items (5)

Numerical implementation of the EDEM for modified Helmholtz BVPs on annular domains ⋮ Spurious eigenvalue-free algorithms of the method of fundamental solutions for solving the Helmholtz equation in bounded multiply connected domains ⋮ The Trefftz method for the Helmholtz equation with degeneracy ⋮ On solution uniqueness of elliptic boundary value problems ⋮ Effective condition number for the finite element method using local mesh refinements

Uses Software

• Mathematica

Cites Work

• Boundary approximation methods for solving elliptic problems on unbounded domains
• A new look at the Lanczos algorithm for solving symmetric systems of linear equations
• Bounds for the maximal eigenvalue of a nonnegative irreducible matrix
• Error and Stability Analysis of Boundary Methods for Elliptic Problems with Interfaces
• Eigenvalues of the Laplacian in Two Dimensions
• Boundary Methods for Solving Elliptic Problems with Singularities and Interfaces
• On the Rate of Convergence of the Bergman–Vekua Method for the Numerical Solution of Elliptic Boundary Value Problems
• Approximations and Bounds for Eigenvalues of Elliptic Operators
• Integral Operators in the Theory of Linear Partial Differential Equations
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