Multigoal-oriented error control for optimal control problems

DI Bernhard Endtmayer BSc

Jan. 22, 2019, 3:30 p.m. S2 054

We consider an optimal control problem subjected to a nonlinear PDE
such as the p-Laplace equation that serves as model problem in our
numerical experiments.
However, we are not primarily interested in the solution itself,
but rather in multiple quantities of interest depending on the solution.
Hence, we derive a posteriori error estimates for all functional at once
using the dual weighted residual (DWR) method.
This is done by combining all quantities of interest to one and applying
the DWR method
for this combined functional. These a posteriori error estimates are
then used
for mesh adaptivity.
Finally, we substantiate our algorithmic development with numerical tests
for the regularized p-Laplace equation. Additionally some recent results
concerning iteration error estimates are presented.