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Goal Oriented Time Adaptivity Using Local Error Estimates

Meisrimel, Peter LU and Birken, Philipp LU (2020) In Algorithms 13.5(113).
Abstract
We consider initial value problems (IVPs) where we are interested in a quantity of interest(QoI) that is the integral in time of a functional of the solution. For these, we analyze goal orientedtime adaptive methods that use only local error estimates. A local error estimate and timestepcontroller for step-wise contributions to the QoI are derived. We prove convergence of the error in theQoI for tolerance to zero under a controllability assumption. By analyzing global error propagationwith respect to the QoI, we can identify possible issues and make performance predictions. Numericaltests verify these results. We compare performance with classical local error based time-adaptivityand a posteriori based adaptivity using the dual-weighted... (More)
We consider initial value problems (IVPs) where we are interested in a quantity of interest(QoI) that is the integral in time of a functional of the solution. For these, we analyze goal orientedtime adaptive methods that use only local error estimates. A local error estimate and timestepcontroller for step-wise contributions to the QoI are derived. We prove convergence of the error in theQoI for tolerance to zero under a controllability assumption. By analyzing global error propagationwith respect to the QoI, we can identify possible issues and make performance predictions. Numericaltests verify these results. We compare performance with classical local error based time-adaptivityand a posteriori based adaptivity using the dual-weighted residual (DWR) method. For dissipativeproblems, local error based methods show better performance than DWR and the goal orientedmethod shows good results in most examples, with significant speedups in some cases. (Less)
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author
and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
time adaptivity, IVPs, error estimation, goal oriented problems
in
Algorithms
volume
13.5
issue
113
publisher
MDPI AG
external identifiers
  • scopus:85085737073
ISSN
1999-4893
DOI
10.3390/a13050113
language
English
LU publication?
yes
id
92494e69-7599-40ad-83eb-43d77af34ee8
date added to LUP
2020-08-18 09:09:54
date last changed
2022-04-19 00:18:22
@article{92494e69-7599-40ad-83eb-43d77af34ee8,
  abstract     = {{We consider initial value problems (IVPs) where we are interested in a quantity of interest(QoI) that is the integral in time of a functional of the solution. For these, we analyze goal orientedtime adaptive methods that use only local error estimates.  A local error estimate and timestepcontroller for step-wise contributions to the QoI are derived. We prove convergence of the error in theQoI for tolerance to zero under a controllability assumption. By analyzing global error propagationwith respect to the QoI, we can identify possible issues and make performance predictions. Numericaltests verify these results. We compare performance with classical local error based time-adaptivityand a posteriori based adaptivity using the dual-weighted residual (DWR) method. For dissipativeproblems, local error based methods show better performance than DWR and the goal orientedmethod shows good results in most examples, with significant speedups in some cases.}},
  author       = {{Meisrimel, Peter and Birken, Philipp}},
  issn         = {{1999-4893}},
  keywords     = {{time adaptivity; IVPs; error estimation; goal oriented problems}},
  language     = {{eng}},
  number       = {{113}},
  publisher    = {{MDPI AG}},
  series       = {{Algorithms}},
  title        = {{Goal Oriented Time Adaptivity Using Local Error Estimates}},
  url          = {{http://dx.doi.org/10.3390/a13050113}},
  doi          = {{10.3390/a13050113}},
  volume       = {{13.5}},
  year         = {{2020}},
}