Advances in Error Estimation and Uncertainty Quantification for Numerical Methods in CEM

We summarize the application of duality-based techniques for error estimation and error control along with uncertainty quantification. The approach yields quality discretizations for estimating uncertain effects in a target quantity of interest (QoI) and naturally extends to the treatment of multiple quantities of interest. By adopting the adjoint approach in both error estimation and uncertainty quantification, expensive computations may be reused. The dual solution enables us to tie changes in the QoI to changes in the discretization, resulting in a significant enhancement of efficiency. We demonstrate examples of the proposed approaches to illustrate the application to scattered quantities of interest.