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Goal Oriented Time Adaptivity Using Local Error Estimates

Centre for Mathematical Sciences, Lund University, Box 118, 22100 Lund, Sweden
Author to whom correspondence should be addressed.
Algorithms 2020, 13(5), 113;
Received: 1 April 2020 / Revised: 24 April 2020 / Accepted: 27 April 2020 / Published: 30 April 2020
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 oriented time adaptive methods that use only local error estimates. A local error estimate and timestep controller for step-wise contributions to the QoI are derived. We prove convergence of the error in the QoI for tolerance to zero under a controllability assumption. By analyzing global error propagation with respect to the QoI, we can identify possible issues and make performance predictions. Numerical tests verify these results. We compare performance with classical local error based time-adaptivity and a posteriori based adaptivity using the dual-weighted residual (DWR) method. For dissipative problems, local error based methods show better performance than DWR and the goal oriented method shows good results in most examples, with significant speedups in some cases. View Full-Text
Keywords: time adaptivity; IVPs; goal oriented problems; error estimation time adaptivity; IVPs; goal oriented problems; error estimation
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Meisrimel, P.; Birken, P. Goal Oriented Time Adaptivity Using Local Error Estimates. Algorithms 2020, 13, 113.

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