Stability analysis of heterogeneous Helmholtz problems and finite element solution based on propagation media approximation

DOI10.1090/mcom/3165zbMath1364.65228OpenAlexW2338955318MaRDI QIDQ2981771

T. Chaumont-Frelet, Christian Gout, Hélène Barucq

Publication date: 10 May 2017

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/mcom/3165

zbMATH Keywords

Helmholtz equationtime-harmonic wavesnumerical resulthigh-order methodstability estimatesoscillatory behaviorhighly heterogeneous mediadepth imagingmedium approximation

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

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Cites Work

• Unnamed Item
• FE heterogeneous multiscale method for long-time wave propagation
• Finite-element heterogeneous multiscale method for the Helmholtz equation
• The discontinuous enrichment method for medium-frequency Helmholtz problems with a spatially variable wavenumber
• Wave interpolation finite elements for Helmholtz problems with jumps in the wave speed
• Variational approach to scattering by unbounded rough surfaces with Neumann and generalized impedance boundary conditions
• Fast Fourier homogenization for elastic wave propagation in complex media
• Stability estimates for a class of Helmholtz problems
• Dispersive and dissipative properties of discontinuous Galerkin finite element methods for the second-order wave equation
• Preasymptotic Error Analysis of CIP-FEM and FEM for Helmholtz Equation with High Wave Number. Part II: $hp$ Version
• Improvements for the ultra weak variational formulation
• Wavenumber Explicit Convergence Analysis for Galerkin Discretizations of the Helmholtz Equation
• Electromagnetic Wave Scattering from Rough Penetrable Layers
• Finite Element Solution of the Helmholtz Equation with High Wave Number Part II: The h-p Version of the FEM
• Convergence analysis for finite element discretizations of the Helmholtz equation with Dirichlet-to-Neumann boundary conditions
• Convergence Analysis of a Discontinuous Galerkin Method with Plane Waves and Lagrange Multipliers for the Solution of Helmholtz Problems
• A variational method for wave scattering from penetrable rough layers
• Discontinuous Galerkin Methods for the Helmholtz Equation with Large Wave Number
• Discrete Dispersion Relation for hp-Version Finite Element Approximation at High Wave Number
• SHARP REGULARITY COEFFICIENT ESTIMATES FOR COMPLEX-VALUED ACOUSTIC AND ELASTIC HELMHOLTZ EQUATIONS
• Pre-asymptotic error analysis of CIP-FEM and FEM for the Helmholtz equation with high wave number. Part I: linear version

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