Efficiency and reliability for the DWR method

DI Bernhard Endtmayer BSc

Dec. 3, 2019, 3:30 p.m. S2 054

In this seminar talk, we derive two-sided a posteriori error estimates for the dual-weightedresidual (DWR) method. We consider single and multiple quantites of interest for estimation. Using a saturation assumption for the quantity of interest, we state lower bounds and upper bounds for the error estimator yielding efficiency and reliability. This is done for large class of nonlinear Problems and nonlinear quantities of interest. We also perform careful studies of the remainder term that is usually neglected. Finally we provide some numerical examples. This work has been supported by the Austrian Science Fund (FWF) under the grant P 29181 GoalOriented Error Control for Phase-Field Fracture Coupled to Multiphysics Problems.