Pre-asymptotic error analysis of \(hp\)-interior penalty discontinuous Galerkin methods for the Helmholtz equation with large wave number
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Publication:2006236
DOI10.1016/j.camwa.2015.06.007zbMath1443.65385OpenAlexW932375325MaRDI QIDQ2006236
Publication date: 8 October 2020
Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.camwa.2015.06.007
stabilityHelmholtz equationlarge wave number\(hp\)-interior penalty discontinuous Galerkin methodspre-asymptotic error estimates
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) Basic methods for problems in optics and electromagnetic theory (78M99)
Related Items (10)
Preasymptotic error analysis of high order interior penalty discontinuous Galerkin methods for the Helmholtz equation with high wave number ⋮ Decompositions of High-Frequency Helmholtz Solutions via Functional Calculus, and Application to the Finite Element Method ⋮ Staggered discontinuous Galerkin methods for the Helmholtz equation with large wave number ⋮ Convergence and Quasi-Optimality of an Adaptive Continuous Interior Penalty Finite Element Method ⋮ A Numerical Analysis of the Weak Galerkin Method for the Helmholtz Equation with High Wave Number ⋮ Superconvergence analysis of linear FEM based on polynomial preserving recovery for Helmholtz equation with high wave number ⋮ A sharp relative-error bound for the Helmholtz \(h\)-FEM at high frequency ⋮ Supercloseness of linear DG-FEM and its superconvergence based on the polynomial preserving recovery for Helmholtz equation ⋮ Unnamed Item ⋮ Convergence and quasi-optimality of an adaptive continuous interior multi-penalty finite element method
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
- A least-squares finite element method for the Helmholtz equation
- The finite element method with non-uniform mesh sizes applied to the exterior Helmholtz problem
- Analysis of continuous formulations underlying the computation of time- harmonic acoustics in exterior domains
- Finite element analysis of acoustic scattering
- An analysis of the discontinuous Galerkin method for wave propagation problems
- Reducing spurious dispersion, anisotropy and reflection in finite element analysis of time-harmonic acoustics
- Eigensolution analysis of the discontinuous Galerkin method with nonuniform grids: I. One space dimension
- 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
- Improved energy estimates for interior penalty, constrained and discontinuous Galerkin methods for elliptic problems. I
- A generalized finite element method for solving the Helmholtz equation in two dimensions with minimal pollution
- A discontinuous finite element formulation for Helmholtz equation
- General DG-methods for highly indefinite Helmholtz problems
- Stability estimates for a class of Helmholtz problems
- Dispersive and dissipative properties of discontinuous Galerkin finite element methods for the second-order wave equation
- Linear continuous interior penalty finite element method for Helmholtz equation With High Wave Number: One-Dimensional Analysis
- Absolutely stable local discontinuous Galerkin methods for the Helmholtz equation with large wave number
- 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
- ℎ𝑝-Discontinuous Galerkin methods for the Helmholtz equation with large wave number
- Wavenumber Explicit Convergence Analysis for Galerkin Discretizations of the Helmholtz Equation
- Sweeping Preconditioner for the Helmholtz Equation: Moving Perfectly Matched 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
- Fully discrete dynamic mesh discontinuous Galerkin methods for the Cahn-Hilliard equation of phase transition
- Continuous interior penalty $hp$-finite element methods for advection and advection-diffusion equations
- Discontinuous Galerkin Methods for the Helmholtz Equation with Large Wave Number
- The Numerical Solution of the Three-Dimensional Inverse Scattering Problem for Time Harmonic Acoustic Waves
- On the Numerical Solutions of Helmholtz’s Equation by the Finite Element Method
- An Interior Penalty Finite Element Method with Discontinuous Elements
- 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
- Computational high frequency wave propagation
- 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
- Finite Element Approximation of Time Harmonic Waves in Periodic Structures
- Preasymptotic Error Analysis of Higher Order FEM and CIP-FEM for Helmholtz Equation with High Wave Number
- Optimal Discontinuous Galerkin Methods for Wave Propagation
- 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
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