Direct and Inverse Problems for PDEs with Random Coefficients - Abstract
Multilevel Monte Carlo methods have recently proven to help reduce the high computational cost of sampling based methods. So far, mainly uniform mesh sequences have been considered. This talk aims to provide insights in the combination of these techniques with adaptive finite element methods to perform adaptive refinement of the mesh hierarchy used in the simulation. Numerical experiments examine the performance of the adaptive methods for a posteriori error control and mesh refinement in Monte Carlo and multilevel Monte Carlo methods with respect to localised goals. Robust heuristics are tested that reconstruct suitable parameters needed for the calculations.