On Goal Oriented Time Adaptivity using Local Error Estimates
(2017) 88th Annual Meeting of GAMM In Proceedings in applied mathematics and mechanics 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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/96a651cf-769e-46ca-9ab8-ed5a484f8242
- author
- Meisrimel, Peter LU and Birken, Philipp LU
- organization
- publishing date
- 2017-12
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- host publication
- PAMM : Proceedings in applied mathematics and mechanics - Proceedings in applied mathematics and mechanics
- series title
- Proceedings in applied mathematics and mechanics
- volume
- 17
- edition
- 1
- pages
- 2 pages
- publisher
- Wiley-VCH Verlag
- conference name
- 88th Annual Meeting of GAMM
- conference location
- Weimar, Germany
- conference dates
- 2017-03-06 - 2017-03-10
- ISSN
- 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
- 2021-01-14 12:47:11
@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> -> 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}}, booktitle = {{PAMM : Proceedings in applied mathematics and mechanics}}, issn = {{1617-7061}}, language = {{eng}}, pages = {{849--850}}, publisher = {{Wiley-VCH Verlag}}, series = {{Proceedings in applied mathematics and mechanics}}, title = {{On Goal Oriented Time Adaptivity using Local Error Estimates}}, url = {{http://dx.doi.org/10.1002/pamm.201710392}}, doi = {{10.1002/pamm.201710392}}, volume = {{17}}, year = {{2017}}, }