On Stability of Discretizations of the Helmholtz Equation
DOI10.1007/978-3-642-22061-6_9zbMath1248.65115arXiv1105.2112OpenAlexW3106381385MaRDI QIDQ2902573
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Publication date: 21 August 2012
Published in: Lecture Notes in Computational Science and Engineering (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1105.2112
stabilityconvergencefinite element methoddiscontinuous Galerkin methodHelmholtz equationleast squares methodmesh refinementlarge wavenumbers
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) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50)
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- Trefftz-based methods for time-harmonic acoustics
- A refined finite element convergence theory for highly indefinite Helmholtz problems
- The h-p version of the finite element method. I. The basic approximation results
- A two-point boundary value problem with a rapidly oscillating solution
- On accuracy conditions for the numerical computation of waves
- Galerkin/least-squares finite element methods for the reduced wave equation with non-reflecting boundary conditions in unbounded domains
- Finite element analysis of acoustic scattering
- The partition of unity finite element method: basic theory and applications
- NETGEN: An advancing front 2D/3D-mesh generator based on abstract rules
- A discontinuous Galerkin method with Lagrange multipliers for the solution of Helmholtz problems in the mid-frequency regime
- Special short wave elements for flow acoustics
- \(hp\)-finite element methods for singular perturbations
- Plane wave approximation of homogeneous Helmholtz solutions
- A least-squares method for the Helmholtz equation
- A generalized finite element method for solving the Helmholtz equation in two dimensions with minimal pollution
- A survey of finite element methods for time-harmonic acoustics
- The generalized finite element method for Helmholtz equation: theory, computation, and open problems
- The Trefftz method for the Helmholtz equation with degeneracy
- Stability estimates for a class of Helmholtz problems
- Dispersive and dissipative properties of discontinuous Galerkin finite element methods for the second-order wave equation
- Absolutely stable local discontinuous Galerkin methods for the Helmholtz equation with large wave number
- On Stability of Discretizations of the Helmholtz Equation
- Using Plane Waves as Base Functions for Solving Time Harmonic Equations with the Ultra Weak Variational Formulation
- Dispersive and Dissipative Behavior of the Spectral Element Method
- Condition number estimates for combined potential integral operators in acoustics and their boundary element discretisation
- 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
- Wavenumber Explicit Convergence Analysis for Galerkin Discretizations of the Helmholtz Equation
- Wavenumber-Explicit $hp$-BEM for High Frequency Scattering
- 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
- Mapping Properties of Combined Field Helmholtz Boundary Integral Operators
- An Exponentially Convergent Nonpolynomial Finite Element Method for Time-Harmonic Scattering from Polygons
- A new frequency-uniform coercive boundary integral equation for acoustic scattering
- Three-dimensional discontinuous Galerkin elements with plane waves and Lagrange multipliers for the solution of mid-frequency Helmholtz problems
- Wave-Number-Explicit Bounds in Time-Harmonic Scattering
- Error estimates for the Ultra Weak Variational Formulation of the Helmholtz equation
- Discontinuous Galerkin Methods for the Helmholtz Equation with Large Wave Number
- Comparison of two wave element methods for the Helmholtz problem
- Plane wave discontinuous Galerkin methods: Analysis of theh-version
- An Observation Concerning Ritz-Galerkin Methods with Indefinite Bilinear Forms
- 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?
- Discrete Dispersion Relation for hp-Version Finite Element Approximation at High Wave Number
- Modelling of short wave diffraction problems using approximating systems of plane waves
- Finite elements using a plane-wave basis for scattering of surface water waves
- Plane-wave basis finite elements and boundary elements for three-dimensional wave scattering
- A Refined Galerkin Error and Stability Analysis for Highly Indefinite Variational Problems
- SHARP REGULARITY COEFFICIENT ESTIMATES FOR COMPLEX-VALUED ACOUSTIC AND ELASTIC HELMHOLTZ EQUATIONS
- An inequality for the reduced wave operator and the justification of geometrical optics
- Higher‐order extensions of a discontinuous Galerkin method for mid‐frequency Helmholtz problems
- Boundary Element Methods