An analysis of discretizations of the Helmholtz equation in \(L^2\) and in negative norms

DOI10.1016/j.camwa.2013.10.005zbMath1350.65123OpenAlexW2045909314MaRDI QIDQ316564

Mohammad Hasan, M. Dambrine

Publication date: 27 September 2016

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2013.10.005

zbMATH Keywords

regularityconvergencefinite element methoderror analysisHelmholtz equationdispersion errorhigh wavenumberhigh-order FEM

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)

Related Items (8)

A first order system least squares method for the Helmholtz equation ⋮ Editorial: High-order finite element approximation for partial differential equations ⋮ A performance study of NURBS-based isogeometric analysis for interior two-dimensional time-harmonic acoustics ⋮ A semi matrix-free twogrid preconditioner for the Helmholtz equation with near optimal shifts ⋮ Decompositions of High-Frequency Helmholtz Solutions via Functional Calculus, and Application to the Finite Element Method ⋮ The surrogate matrix methodology: accelerating isogeometric analysis of waves ⋮ Towards accuracy and scalability: combining isogeometric analysis with deflation to obtain scalable convergence for the Helmholtz equation ⋮ Dispersion-optimized quadrature rules for isogeometric analysis: modified inner products, their dispersion properties, and optimally blended schemes

Uses Software

• Netgen
• NGSolve

Cites Work

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