Wavenumber explicit analysis of a DPG method for the multidimensional Helmholtz equation

DOI10.1016/j.cma.2011.11.024zbMath1243.76059OpenAlexW2080631773MaRDI QIDQ438126

J. Zitelli, Jayadeep Gopalakrishnan, Ignacio Muga, Leszek F. Demkowicz

Publication date: 20 July 2012

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://pdxscholar.library.pdx.edu/mth_fac/39

zbMATH Keywords

robustnessdispersionphase errorhigh frequencyPetrov Galerkin methodtime harmonic wave propagation

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) 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) Hydro- and aero-acoustics (76Q05) Finite element methods applied to problems in fluid mechanics (76M10) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

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Cites Work

• Unnamed Item
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• A class of discontinuous Petrov-Galerkin methods. III: Adaptivity
• A class of discontinuous Petrov-Galerkin methods. IV: The optimal test norm and time-harmonic wave propagation in 1D
• A class of discontinuous Petrov-Galerkin methods. I: The transport equation
• Finite element analysis of acoustic scattering
• Wave-ray multigrid method for standing wave equations
• Computational aspects of the ultra-weak variational formulation
• Commuting smoothed projectors in weighted norms with an application to axisymmetric Maxwell equations
• An analysis of the practical DPG method
• A class of discontinuous Petrov-Galerkin methods. II. Optimal test functions
• Optimally Blended Spectral-Finite Element Scheme for Wave Propagation and NonStandard Reduced Integration
• Plane Wave Discontinuous Galerkin Methods for the 2D Helmholtz Equation: Analysis of the p-Version
• ℎ𝑝-Discontinuous Galerkin methods for the Helmholtz equation with large wave number
• Analysis of the DPG Method for the Poisson Equation
• Convergence analysis for finite element discretizations of the Helmholtz equation with Dirichlet-to-Neumann boundary conditions
• Three-dimensional discontinuous Galerkin elements with plane waves and Lagrange multipliers for the solution of mid-frequency Helmholtz problems
• Discontinuous Galerkin Methods for the Helmholtz Equation with Large Wave Number
• Application of an Ultra Weak Variational Formulation of Elliptic PDEs to the Two-Dimensional Helmholtz Problem
• Is the Pollution Effect of the FEM Avoidable for the Helmholtz Equation Considering High Wave Numbers?
• First-Order System Least-Squares for the Helmholtz Equation