Goal Oriented Time Adaptivity Using Local Error Estimates

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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.
Original languageEnglish
JournalAlgorithms
Volume13.5
Issue number113
DOIs
Publication statusPublished - 2020 Jun

Subject classification (UKÄ)

  • Computational Mathematics

Keywords

  • time adaptivity
  • IVPs
  • error estimation
  • goal oriented problems

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