Publications

PDE-constrained optimal control problems require regularisation to ensure well-posedness, introducing small perturbations that make the solutions challenging to approximate accurately. We propose a finite element approach that couples both regularisation and discretisation adaptivity, varying both the regularisation parameter and mesh-size locally based on rigorous a posteriori error estimates aiming to dynamically balance induced regularisation and discretisation errors, offering a robust and efficient method for solving these problems. We demonstrate the efficacy of our analysis with several numerical experiments.

A significant portion of Landslide Early Warning Systems (LEWS) relies on the definition of operational thresholds and the monitoring of cumulative rainfall for alert issuance. These thresholds can be obtained in various ways, but most often they are based on previous landslide data. This approach introduces several limitations. For instance, there is a requirement for the location to have been previously monitored in some way to have this type of information recorded. Another significant limitation is the need for information regarding the location and timing of incidents. Despite the current ease of obtaining location information (GPS, drone images, etc.), the timing of the event remains challenging to ascertain for a considerable portion of landslide data. Concerning rainfall monitoring, there are multiple ways to consider it, for instance, examining accumulations over various intervals (1 h, 6 h, 24 h, 72 h), as well as in the calculation of effective rainfall, which represents the precipitation that actually infiltrates the soil. However, in the vast majority of cases, both the thresholds and the rain monitoring approach are defined manually and subjectively, relying on the operators’ experience. This makes the process labor-intensive and time-consuming, hindering the establishment of a truly standardized and rapidly scalable methodology on a large scale. In this work, we propose a Landslides Early Warning System (LEWS) based on the concept of rainfall half-life and the determination of thresholds using Cluster Analysis and data inversion. The system is designed to be applied in extensive monitoring networks, such as the one utilized by Cemaden, Brazil’s National Center for Monitoring and Early Warning of Natural Disasters.