Arezou Ghesmati

Arezou Ghesmati, Wolfgang Bangerth, Bruno Turcksin

We derive a residual-based a posteriori error estimator for the conforming hp-Adaptive Finite Element Method (hp-AFEM) for the steady state Stokes problem describing the slow motion of an incompressible fluid. This error estimator is obtained by extending the idea of a posteriori error estimation for the classical $h$-version of AFEM. We also establish the reliability and efficiency of the error estimator. The proofs are based on the well-known Clement-type interpolation operator introduced in 2005 in the context of the hp-AFEM. Numerical experiments show the performance of an adaptive hp-FEM algorithm using the proposed a posteriori error estimator.

Oskar Triebe, Fletcher Passow, Simon Wittner et al.

The reliability of local power grid infrastructure is challenged by sustainable energy developments increasing electric load uncertainty. Transmission System Operators (TSOs) need load forecasts of higher spatial resolution, extending current forecasting operations from zonal aggregates to individual nodes. However, nodal loads are less accurate to forecast and require a large number of individual forecasts, which are hard to manage for the human experts assessing risks in the control room's daily operations (operator). In collaboration with a TSO, we design a multi-level system that meets the needs of operators for hourly day-ahead load forecasting. Utilizing a uniquely extensive dataset of zonal and nodal net loads, we experimentally evaluate our system components. First, we develop an interpretable and scalable forecasting model that allows for TSOs to gradually extend zonal operations to include nodal forecasts. Second, we evaluate solutions to address the heterogeneity and volatility of nodal load, subject to a trade-off. Third, our system is manageable with a fully parallelized single-model forecasting workflow. Our results show accuracy and interpretability improvements for zonal forecasts, and substantial improvements for nodal forecasts. In practice, our multi-level forecasting system allows operators to adjust forecasts with unprecedented confidence and accuracy, and to diagnose otherwise opaque errors precisely.