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On Goal Oriented Time Adaptivity using Local Error Estimates

Meisrimel, Peter LU and Birken, Philipp LU (2017) 88th Annual Meeting of GAMM 17. p.849-850
Abstract
We consider adaptive time discretization methods for ordinary differential equations where one aims to control the error in a quantity of interest of the form J(u) = ∫ j(u(t))dt with j : Rd -> R. In this setting we propose a new timestep controller based on local error estimates of the quantity of interest. The new method converges when the tolerance goes to zero.We experimentally compare the new scheme with the classic norm-based time-adaptivity based on local error estimates as well as the dual-weighted residual (DWR) method. The results show significantly lower efficiency for the DWR method. The local error based schemes are similarly efficient, with the new scheme showing significant improvement in some cases.
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author
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
host publication
PAMM
volume
17
pages
2 pages
publisher
Wiley Online Library
conference name
88th Annual Meeting of GAMM
conference location
Weimar, Germany
conference dates
2017-03-06 - 2017-03-10
ISBN
1617-7061
DOI
10.1002/pamm.201710392
language
English
LU publication?
yes
id
96a651cf-769e-46ca-9ab8-ed5a484f8242
date added to LUP
2018-03-16 14:17:55
date last changed
2018-11-21 21:38:40
@inproceedings{96a651cf-769e-46ca-9ab8-ed5a484f8242,
  abstract     = {We consider adaptive time discretization methods for ordinary differential equations where one aims to control the error in a quantity of interest of the form J(u) = ∫ j(u(t))dt with j : R<sup>d</sup> -&gt; R. In this setting we propose a new timestep controller based on local error estimates of the quantity of interest. The new method converges when the tolerance goes to zero.We experimentally compare the new scheme with the classic norm-based time-adaptivity based on local error estimates as well as the dual-weighted residual (DWR) method. The results show significantly lower efficiency for the DWR method. The local error based schemes are similarly efficient, with the new scheme showing significant improvement in some cases.},
  author       = {Meisrimel, Peter and Birken, Philipp},
  isbn         = {1617-7061},
  language     = {eng},
  location     = {Weimar, Germany},
  pages        = {849--850},
  publisher    = {Wiley Online Library},
  title        = {On Goal Oriented Time Adaptivity using Local Error Estimates},
  url          = {http://dx.doi.org/10.1002/pamm.201710392},
  volume       = {17},
  year         = {2017},
}