Sharp preasymptotic error bounds for the Helmholtz \(h\)-FEM

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Cites Work

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Finite element analysis of acoustic scattering
On the existence and convergence of the solution of PML equations
The Helmholtz equation in heterogeneous media: a priori bounds, well-posedness, and resonances
Finite element solution of the Helmholtz equation with high wave number. I: The \(h\)-version of the FEM
A sharp relative-error bound for the Helmholtz \(h\)-FEM at high frequency
Wavenumber-explicit convergence analysis for finite element discretizations of time-harmonic wave propagation problems with perfectly matched layers
Wavenumber-explicit convergence of the \(hp\)-FEM for the full-space heterogeneous Helmholtz equation with smooth coefficients
Uniform a priori estimates for elliptic problems with impedance boundary conditions
Analysis of the PML equations in general convex geometry
Preasymptotic error analysis of CIP-FEM and FEM for Helmholtz equation with high wave number. II: \(hp\) version
On Stability of Discretizations of the Helmholtz Equation
Stability analysis of heterogeneous Helmholtz problems and finite element solution based on propagation media approximation
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 finite PML approximation for the three dimensional time-harmonic Maxwell and acoustic scattering problems
Wave-Number-Explicit Bounds in Time-Harmonic Scattering
Discontinuous Galerkin Methods for the Helmholtz Equation with Large Wave Number
The Perfectly Matched Layer in Curvilinear Coordinates
Solving Time-Harmonic Scattering Problems Based on the Pole Condition II: Convergence of the PML Method
FEM and CIP-FEM for Helmholtz Equation with High Wave Number and Perfectly Matched Layer Truncation
Wavenumber explicit convergence analysis for finite element discretizations of general wave propagation problems
Stability and finite element error analysis for the Helmholtz equation with variable coefficients
Preasymptotic Error Analysis of Higher Order FEM and CIP-FEM for Helmholtz Equation with High Wave Number
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
Acoustic and electromagnetic equations. Integral representations for harmonic problems
Perfectly-Matched-Layer Truncation is Exponentially Accurate at High Frequency
Decompositions of High-Frequency Helmholtz Solutions via Functional Calculus, and Application to the Finite Element Method
Wavenumber-explicit stability and convergence analysis of \(hp\) finite element discretizations of Helmholtz problems in piecewise smooth media

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