A Numerical Analysis of the Weak Galerkin Method for the Helmholtz Equation with High Wave Number
From MaRDI portal
Publication:5159050
DOI10.4208/cicp.OA-2016-0121zbMath1488.65610OpenAlexW2610875178MaRDI QIDQ5159050
Publication date: 26 October 2021
Published in: Communications in Computational Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.4208/cicp.oa-2016-0121
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) Waves and radiation in optics and electromagnetic theory (78A40)
Related Items (17)
Convergence of an adaptive modified WG method for second-order elliptic problem ⋮ A Posteriori Error Estimates for a Modified Weak Galerkin Finite Element Approximation of Second Order Elliptic Problems with DG Norm ⋮ Convergence and optimality of an adaptive modified weak Galerkin finite element method ⋮ A fictitious domain spectral method for solving the Helmholtz equation in exterior domains ⋮ A modified weak Galerkin method for \(\boldsymbol{H}(\mathrm{curl})\)-elliptic problem ⋮ The lowest-order stabilizer free weak Galerkin finite element method ⋮ Weak Galerkin finite element with curved edges ⋮ Weak Galerkin finite element method for linear poroelasticity problems ⋮ Staggered discontinuous Galerkin methods for the Helmholtz equation with large wave number ⋮ A new upwind weak Galerkin finite element method for linear hyperbolic equations ⋮ A priori and a posteriori error estimates of the weak Galerkin finite element method for parabolic problems ⋮ The Weak Galerkin Method for Elliptic Eigenvalue Problems ⋮ Weak Galerkin finite element method for a class of quasilinear elliptic problems ⋮ A curl-conforming weak Galerkin method for the quad-curl problem ⋮ Convergence of adaptive weak Galerkin finite element methods for second order elliptic problems ⋮ A sharp relative-error bound for the Helmholtz \(h\)-FEM at high frequency ⋮ Unnamed Item
Cites Work
- Unnamed Item
- Unnamed Item
- Preasymptotic error analysis of high order interior penalty discontinuous Galerkin methods for the Helmholtz equation with high wave number
- Wavenumber explicit analysis of a DPG method for the multidimensional Helmholtz equation
- A weak Galerkin finite element scheme for the biharmonic equations by using polynomials of reduced order
- A class of discontinuous Petrov-Galerkin methods. IV: The optimal test norm and time-harmonic wave propagation in 1D
- A weak Galerkin finite element method for the Maxwell equations
- 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
- Finite element solution of the Helmholtz equation with high wave number. I: The \(h\)-version of the FEM
- A weak Galerkin finite element method for second-order elliptic problems
- 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
- 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
- A new weak Galerkin finite element method for the Helmholtz equation
- ℎ𝑝-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
- Analysis of a Spectral-Galerkin Approximation to the Helmholtz Equation in Exterior Domains
- Discontinuous Galerkin Methods for the Helmholtz Equation with Large Wave Number
- An Observation Concerning Ritz-Galerkin Methods with Indefinite Bilinear Forms
- 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?
- Discrete Dispersion Relation for hp-Version Finite Element Approximation at High Wave Number
- Finite Element Methods for Maxwell's Equations
- Weak Galerkin finite element methods for elliptic PDEs
- Preasymptotic Error Analysis of Higher Order FEM and CIP-FEM for Helmholtz Equation with High Wave Number
- A Numerical Study on the Weak Galerkin Method for the Helmholtz Equation
- A New Weak Galerkin Finite Element Scheme for the Brinkman Model
- The Mathematical Theory of Finite Element Methods
- Pre-asymptotic error analysis of CIP-FEM and FEM for the Helmholtz equation with high wave number. Part I: linear version
This page was built for publication: A Numerical Analysis of the Weak Galerkin Method for the Helmholtz Equation with High Wave Number
