Christian Sellmann, M. Sc.

In many applications, predicting both the spatial and temporal behavior of a physical quantity is crucial. Typically, this is done by examining the system's development at discrete points in time.

In the context of “space-time modeling“, time is considered as additional dimension, and the physical problem is solved holistically for both space and time. This approach creates great flexibility in discretization, as the number of time points considered can vary for different areas. However, it also increases the complexity of the problem, as a four-dimensional problem must be solved depending. We at IKM develop novel versions of the Virtual Element Method (VEM) for a holistic space-time discretization. These offer high flexibility in meshing the solution domain, particularly highlighting the potential of using error estimators. Through these, the efficiency and reliability of the solution can be enhanced. For example, the use of error estimators makes it possible to refine the (temporal) mesh resolution only in regions that are important for calculating the sought-after physical quantities.