The weak element method applied to Helmholtz type equations

DOI10.1016/0168-9274(86)90043-7zbMath0611.65070OpenAlexW1967101574MaRDI QIDQ1087323

Charles I. Goldstein

Publication date: 1986

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0168-9274(86)90043-7

zbMATH Keywords

error estimatesscatteringfinite elementdiffractionexponential basis functionstwo-dimensional Helmholtz equationhighly oscillatory solutionintermediate frequency rangeweak elements

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) Diffraction, scattering (78A45) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items

A survey of finite element methods for time-harmonic acoustics, A discontinuous finite element formulation for Helmholtz equation, A compact fourth order scheme for the Helmholtz equation in polar coordinates, A discontinuous Galerkin method with Lagrange multipliers for the solution of Helmholtz problems in the mid-frequency regime, A Survey of Trefftz Methods for the Helmholtz Equation, Solution of Helmholtz equation by differential quadrature method, The extended/generalized finite element method: An overview of the method and its applications, Adaptive numerical solution of a discontinuous Galerkin method for a Helmholtz problem in low-frequency regime, Higher-order meshing of implicit geometries. I: Integration and interpolation in cut elements, Dispersion Analysis of the Discontinuous Enrichment Method for Plane-strain Elasticity, Learning dominant wave directions for plane wave methods for high-frequency Helmholtz equations, Development of a sixth-order two-dimensional convection-diffusion scheme via Cole-Hopf transformation, A fourth-order compact scheme for the Helmholtz equation: Alpha-interpolation of FEM and FDM stencils

Cites Work

• Unnamed Item
• Unnamed Item
• The numerical solution of the Helmholtz equation for wave propagation problems in underwater acoustics
• Finite element methods applied to nearly one-way wave propagation
• A two-point boundary value problem with a rapidly oscillating solution
• On accuracy conditions for the numerical computation of waves
• The finite element method with non-uniform mesh sizes applied to the exterior Helmholtz problem
• Weak-element approximations to elliptic differential equations
• A numerical method for the exterior Dirichlet problem for the reduced wave equation