Abstract2018-05-24T12:52:58+00:00

A simple strategy to assess the error in the numerical wave number of the Finite Element solution of the Helmholtz equation

Author (s): Steffens, L.M.,Díez, P.
Journal: Computer Methods in Applied Mechanics and Engineering

Volume: 198, Issues 15-16
Pages: 1389 – 1400
Date: 2009

Abstract:

The standard approach for
goal oriented error estimation and adaptivity uses an error representation via
an adjoint problem, based on the linear functional output representing the
quantity of interest. For the assessment of the error in the approximation of
the wave number for the Helmholtz problem (also referred to as dispersion or
pollution error), this strategy cannot be applied. This is because there is no
linear extractor producing the wave number from the solution of the acoustic
problem. Moreover, in this context, the error assessment paradigm is reverted
in the sense that the exact value of the wave number,
κ,
is known (it is part of the problem data) and the effort produced in the error assessment
technique aims at obtaining the numerical wave number,
κH, as a postprocess of the numerical
solution,
uH The strategy introduced in this paper is based on the ideas
used in the a priori analysis. A modified equation corresponding to a modified
wave number
κm is introduced. Then, the value of κm such that the modified problem better
accommodates the numerical solution
uH is
taken as the estimate of the numerical wave number
κH . Thus, both global and local versions of
the error estimator are proposed. The obtained estimates of the dispersion
error match the a priori predicted dispersion error and, in academical
examples, the actual values of the error in the wave number.

 

  
  

Bibtex:

@article{Steffens20091389,
author = "Steffens, L.M. and Díez, P.",
title = "A simple strategy to assess the error in the numerical wave number of the finite element solution of the Helmholtz equation ",
journal = "Computer Methods in Applied Mechanics and Engineering ",
volume = "198",
number = "15–16",
pages = "1389 - 1400",
year = "2009",
issn = "0045-7825",
doi = "http://dx.doi.org/10.1016/j.cma.2008.12.005",
url = "http://www.sciencedirect.com/science/article/pii/S004578250800426X",
}