Explicit residual-based a posteriori error estimation for finite element discretizations of the Helmholtz equation: Computation of the constant and new measures of error estimator quality
type: Item
instance of: scholarly article
title: Explicit residual-based a posteriori error estimation for finite element discretizations of the Helmholtz equation: Computation of the constant and new measures of error estimator quality
zbMATH Open document ID: 0887.76040
DOI: 10.1016/0045-7825(95)00953-1
author: James R. Stewart
author: T. J. R. Hughes
published in: Computer Methods in Applied Mechanics and Engineering
publication date: 1998-06-01T00:00:00Z
review text: This paper continues the study of an explicit residual-based a posteriori error estimator developed for finite element discretizations of the Helmholtz equation, in the context of time-harmonic exterior acoustics problems. A methodology is established for computing error estimates; these error estimates are then analyzed in detail. The error estimates are made possible by computing the (scaling) constant, which exists in error estimators of this type. In our case, this constant is difficult to obtain. An algorithm for computing the constant is described. (It is noted that the error indicators used for adaptive computations do not require knowledge of this constant.) Several measures are used to analyze the quality of the error estimates, providing a complete description of the error estimator in the context of these problems. We compute global effectivity indices, and utilize the local (element-wise) effectivity index in computing three additional measures. The analysis of the error estimator is carried out on relatively coarse meshes, typical of those used in practical engineering computations.
Mathematics Subject Classification ID: 76M10
Mathematics Subject Classification ID: 76Q05
zbMATH DE Number: 1081958
zbMATH Keywords: local effectivity index
zbMATH Keywords: robustness index
zbMATH Keywords: time-harmonic exterior acoustics problems
zbMATH Keywords: global effectivity indices
zbMATH Keywords: coarse meshes
MaRDI profile type: Publication
full work available at URL: 0045-7825(95)00953-1
OpenAlex ID: W2091220377
cites work: An a posteriori error estimator and \(hp\)-adaptive strategy for finite element discretizations of the Helmholtz equation in exterior domains
cites work: \(h\)-adaptive finite element computation of time-harmonic exterior acoustics problems in two dimensions
cites work: Adaptive finite element methods in computational mechanics
cites work: An Adaptive Finite Element Method for Linear Elliptic Problems
cites work: Adaptive finite element methods for diffusion and convection problems
cites work: Error Estimates and Automatic Time Step Control for Nonlinear Parabolic Problems, I
cites work: Adaptive techniques for the contact of elastic bodies
cites work: Galerkin/least-squares finite element methods for the reduced wave equation with non-reflecting boundary conditions in unbounded domains
cites work: Finite element methods for the Helmholtz equation in an exterior domain: Model problems
cites work: Q4326989
cites work: A Galerkin least‐squares finite element method for the two‐dimensional Helmholtz equation
cites work: A new finite element formulation for computational fluid dynamics. VIII. The Galerkin/least-squares method for advective-diffusive equations
cites work: A new finite element formulation for computational fluid dynamics. IX: Fourier analysis of space-time Galerkin/least-squares algorithms
cites work: Is the Pollution Effect of the FEM Avoidable for the Helmholtz Equation Considering High Wave Numbers?
cites work: Pollution-error in the \(h\)-version of the finite-element method and the local quality of a posteriori error estimators
cites work: A posteriori estimation and adaptive control of the pollution error in the h‐version of the finite element method
cites work: Local and pollution error estimation for finite element approximations of elliptic boundary value problems
cites work: Validation of a posteriori error estimators by numerical approach
cites work: Exact non-reflecting boundary conditions
cites work: Studies of domain‐based formulations for computing exterior problems of acoustics
cites work: Q3890207
cites work: Adaptive remeshing for compressible flow computations
description: scientific article; zbMATH DE number 1081958