Residual-Based Adaptivity and PWDG Methods for the Helmholtz Equation

DOI10.1137/140967696zbMath1433.65300arXiv1405.1957OpenAlexW2963663139MaRDI QIDQ5264142

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Publication date: 20 July 2015

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1405.1957

zbMATH Keywords

Helmholtz equationresidual a posteriori error indicatorsplane wave discontinuous Galerkin (PWDG) method

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory (78M10) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50) Variational methods for second-order elliptic equations (35J20)

Related Items (12)

Adaptive refinement for \(hp\)-version Trefftz discontinuous Galerkin methods for the homogeneous Helmholtz problem ⋮ A plane wave discontinuous Galerkin method with a Dirichlet-to-Neumann boundary condition for the scattering problem in acoustics ⋮ Peter Monk's contributions to numerical analysis and Maxwell's equations ⋮ Least-squares Padé approximation of parametric and stochastic Helmholtz maps ⋮ Global space-time Trefftz DG schemes for the time-dependent linear wave equation ⋮ Adaptive FEM for Helmholtz equation with large wavenumber ⋮ A Survey of Trefftz Methods for the Helmholtz Equation ⋮ Robust Adaptive $hp$ Discontinuous Galerkin Finite Element Methods for the Helmholtz Equation ⋮ A plane wave least squares method for the Maxwell equations in anisotropic media ⋮ A comparison of high-order polynomial and wave-based methods for Helmholtz problems ⋮ A combined scheme of the local spectral element method and the generalized plane wave discontinuous Galerkin method for the anisotropic Helmholtz equation ⋮ Generalized plane wave discontinuous Galerkin methods for nonhomogeneous Helmholtz equations with variable wave numbers

Cites Work

• Plane wave discontinuous Galerkin methods: exponential convergence of the \(hp\)-version
• The ultra weak variational formulation of thin clamped plate problems
• Solving Maxwell's equations using the ultra weak variational formulation
• A local wave tracking strategy for efficiently solving mid- and high-frequency Helmholtz problems
• General DG-methods for highly indefinite Helmholtz problems
• Trefftz discontinuous Galerkin methods for acoustic scattering on locally refined meshes
• Error estimates for the ultra weak variational formulation in linear elasticity
• On Stability of Discretizations of the Helmholtz Equation
• Improvements for the ultra weak variational formulation
• Dispersion analysis of plane wave discontinuous Galerkin methods
• Plane Wave Discontinuous Galerkin Methods for the 2D Helmholtz Equation: Analysis of the p-Version
• Error estimates for the Ultra Weak Variational Formulation of the Helmholtz equation
• Plane wave discontinuous Galerkin methods: Analysis of theh-version
• A comparison of adaptive refinement techniques for elliptic problems
• Application of an Ultra Weak Variational Formulation of Elliptic PDEs to the Two-Dimensional Helmholtz Problem
• A Convergent Adaptive Algorithm for Poisson’s Equation
• Error analysis of Trefftz-discontinuous Galerkin methods for the time-harmonic Maxwell equations
• A hybrid numerical asymptotic method for scattering problems

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