Error estimates of the DtN finite element method for the exterior Helmholtz problem

DOI10.1016/j.cam.2005.12.004zbMath1171.65437OpenAlexW2012366149MaRDI QIDQ859860

Daisuke Koyama

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.2005.12.004

zbMATH Keywords

finite element methodDirichlet-to-Neumann operatorartificial boundary conditionexterior Helmholtz problempriori error estimate

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items (19)

Error estimates of the finite element method for the exterior Helmholtz problem with a modified DtN boundary condition ⋮ The superconvergence of composite Newton-Cotes rules for Hadamard finite-part integral on a circle ⋮ A fast numerical method for a natural boundary integral equation for the Helmholtz equation ⋮ A priori error estimates of the dtn-FEM for the transmission problem in acoustics ⋮ The factorization method for the inverse scattering problem from thin dielectric objects ⋮ A plane wave discontinuous Galerkin method with a Dirichlet-to-Neumann boundary condition for the scattering problem in acoustics ⋮ A radiation and propagation problem for a Helmholtz equation with a compactly supported nonlinearity ⋮ Error analysis of the DtN-FEM for the scattering problem in acoustics via Fourier analysis ⋮ Numerical solution of a certain hypersingular integral equation of the first kind ⋮ Coupling BEM with FEM by a direct computation of the boundary stiffness matrix ⋮ An a priori error estimate of the Dirichlet-to-Neumann finite element method for multiple scattering problems ⋮ A survey on artificial boundary method ⋮ An adaptive coupling method for exterior anisotropic elliptic problems ⋮ A Schwarz alternating algorithm for a three-dimensional exterior harmonic problem with prolate spheroid boundary ⋮ The superconvergence of composite trapezoidal rule for Hadamard finite-part integral on a circle and its application ⋮ A natural BEM with non-uniform grids on the elliptic boundary and its coupling method ⋮ Finite Elements for Helmholtz Equations with a Nonlocal Boundary Condition ⋮ Unnamed Item ⋮ The factorization method for a partially coated cavity in inverse scattering

Cites Work

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• Numerical solution for exterior problems
• Exact non-reflecting boundary conditions
• A finite element method for exterior interface problems
• Analysis of continuous formulations underlying the computation of time- harmonic acoustics in exterior domains
• Variational methods for underwater acoustic problems
• Finite element analysis of acoustic scattering
• Finite element analysis for the eigenvalue problem of the linear water wave in a water region with a reentrant corner
• A finite-element capacitance matrix method for exterior Helmholtz problems
• High-order boundary conditions and finite elements for infinite domains
• A controllability method with an artificial boundary condition for the exterior Helmholtz problem
• The Localized Finite Element Method and Its Application to the Two-Dimensional Sea-Keeping Problem
• A Finite Element Method for Solving Helmholtz Type Equations in Waveguides and Other Unbounded Domains
• The Approximation of the Exact Boundary Conditions at an Artificial Boundary for Linear Elastic Equations and its Application
• An Observation Concerning Ritz-Galerkin Methods with Indefinite Bilinear Forms
• Error Estimates for the Finite Element Approximation of Problems in Unbounded Domains
• Curved Elements in the Finite Element Method. I
• Finite Element Approximation of Time Harmonic Waves in Periodic Structures
• An FEM-CSM combined method for planar exterior Laplace problems

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