Preasymptotic error analysis of high order interior penalty discontinuous Galerkin methods for the Helmholtz equation with high wave number
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Publication:293100
DOI10.1007/s10915-015-0074-8zbMath1353.65112OpenAlexW965078348MaRDI QIDQ293100
Publication date: 9 June 2016
Published in: Journal of Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10915-015-0074-8
Helmholtz equationnumerical testhigh wave numberinterior penalty discontinuous Galerkin methodpreasymptotic error estimates
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)
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Cites Work
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- Wavenumber explicit analysis of a DPG method for the multidimensional Helmholtz equation
- A class of discontinuous Petrov-Galerkin methods. IV: The optimal test norm and time-harmonic wave propagation in 1D
- Discontinuous Galerkin approximation with discrete variational principle for the nonlinear Laplacian
- Finite element analysis of acoustic scattering
- Complex wavenumber Fourier analysis of the \(p\)-version finite element method
- Reducing spurious dispersion, anisotropy and reflection in finite element analysis of time-harmonic acoustics
- Elliptic partial differential equations of second order
- Dispersive and dissipative behaviour of high order discontinuous Galerkin finite element methods
- Finite element solution of the Helmholtz equation with high wave number. I: The \(h\)-version of the FEM
- Pre-asymptotic error analysis of \(hp\)-interior penalty discontinuous Galerkin methods for the Helmholtz equation with large wave number
- A generalized finite element method for solving the Helmholtz equation in two dimensions with minimal pollution
- General DG-methods for highly indefinite Helmholtz problems
- Stability estimates for a class of Helmholtz problems
- Linear continuous interior penalty finite element method for Helmholtz equation With High Wave Number: One-Dimensional Analysis
- Preasymptotic Error Analysis of CIP-FEM and FEM for Helmholtz Equation with High Wave Number. Part II: $hp$ Version
- A Hybridizable Discontinuous Galerkin Method for the Helmholtz Equation with High Wave Number
- âđ-Discontinuous Galerkin methods for the Helmholtz equation with large wave number
- Wavenumber Explicit Convergence Analysis for Galerkin Discretizations of the Helmholtz Equation
- 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
- Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations
- Analysis of a Spectral-Galerkin Approximation to the Helmholtz Equation in Exterior Domains
- Discontinuous Galerkin Methods for the Helmholtz Equation with Large Wave Number
- Discrete functional analysis tools for Discontinuous Galerkin methods with application to the incompressible NavierâStokes equations
- An Interior Penalty Finite Element Method with Discontinuous Elements
- Interior Estimates for Ritz-Galerkin Methods
- An Observation Concerning Ritz-Galerkin Methods with Indefinite Bilinear Forms
- Finite Element Methods for Elliptic Equations Using Nonconforming Elements
- Radiation boundary conditions for acoustic and elastic wave calculations
- APPROXIMATION OF SCALAR WAVES IN THE SPACE-FREQUENCY DOMAIN
- Is the Pollution Effect of the FEM Avoidable for the Helmholtz Equation Considering High Wave Numbers?
- Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
- Discrete Dispersion Relation for hp-Version Finite Element Approximation at High Wave Number
- Finite Element Methods for Maxwell's Equations
- Discrete gevrey regularity attractors and uppersâsemicontinuity for a finite difference approximation to the ginzburgâlandau equation
- Interior Regularity Estimates for Elliptic Systems of Difference Equations
- Preasymptotic Error Analysis of Higher Order FEM and CIP-FEM for Helmholtz Equation with High Wave Number
- The Mathematical Theory of Finite Element Methods
- 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
- Nonconforming Elements in the Finite Element Method with Penalty
- Discontinuous Galerkin method applied to a single phase flow in porous media. II
- Discontinuous Galerkin finite element differential calculus and applications to numerical solutions of linear and nonlinear partial differential equations
