Licensiate Defense Peter Meisrimel: "Goal Oriented Time Adaptivity using Local Error Estimates"
Opponent: David Cohen, U Umeå
Examinator: Eskil Hansen, Lund
In many practical applications that require numerical simulations, one is only interested in a lower-dimensional result derived from the solution - a quantity of interest (QoI). Examples
are critical components in larger structures or derived quantities such as average energy production for a wind-turbine.
We consider initial value problems where we are interested in a QoI that is the integral in time of a functional of the solution. For these, we look into local error based time
adaptivity. We derive goal oriented error estimates involving both the time-integration and quadrature error from discretizing the QoI and use these to construct a timestep controller.
For the resulting method we prove convergence of the error in the QoI for tolerance to zero under weak assumptions. We analyze global error propagation of this method and derive
guidelines to predict performance. In numerical tests we verify the convergence results and guidelines on method performance. Additionally, we compare performance with the dual-
weighted residual method (DWR) and classical local error based time-adaptivity. The local error based methods perform better than DWR and the goal oriented method shows good
results in most examples, with significant speedups in some cases.