Time‐dependent Maxwell's equations govern electromagnetics. Under certain conditions, we can rewrite these equations into a partial differential equation of second order, which in this case is the vectorial wave equation. For the vectorial wave equation, we examine numerical schemes and their challenges. For this purpose, we consider a space‐time variational setting, that is, time is just another spatial dimension. More specifically, we apply integration by parts in time as well as in space, leading to a space‐time variational formulation with different trial and test spaces. Conforming discretizations of tensor‐product type result in a Galerkin–Petrov finite element method that requires a CFL condition for stability which we study. To overcome the CFL condition, we use a Hilbert‐type transformation that leads to a variational formulation with equal trial and test spaces. Conforming space‐time discretizations result in a new Galerkin–Bubnov finite element method that is unconditionally stable. In numerical examples, we demonstrate the effectiveness of this Galerkin–Bubnov finite element method. Furthermore, we investigate different projections of the right‐hand side and their influence on the convergence rates. This paper is the first step toward a more stable computation and a better understanding of vectorial wave equations in a conforming space‐time approach.

The ability to deal with complex geometries and to go to higher orders is the main advantage of space-time finite element methods. Therefore, we want to develop a solid background from which we can construct appropriate space-time methods. In this paper, we will treat time as another space direction, which is the main idea of space-time methods. First, we will briefly discuss how exactly the vectorial wave equation is derived from Maxwell’s equations in a space-time structure, taking into account Ohm’s law. Then we will derive a space-time variational formulation for the vectorial wave equation using different trial and test spaces. This paper has two main goals. First, we prove unique solvability for the resulting Galerkin–Petrov variational formulation. Second, we analyze the discrete equivalent of the equation in a tensor product and show conditional stability, i.e., under a CFL condition. Understanding the vectorial wave equation and the corresponding space-time finite element methods is crucial for improving the existing theory of Maxwell’s equations and paves the way to computations of more complicated electromagnetic problems.

Intentional and unintentional GNSS interference can greatly affect the performance of precise timing and localization in areas such as automated driving or aviation. Nevertheless, reports show that jamming occurs near many European airports that are located close to a highway or in heavy industry areas due to broadcasting of interfering signals. To assess the impact of such potential risks, we investigated interference occurring on a section of highway located both near to an airport and close to logistics centers as part of the Austrian Security Research Program project CATCH-IN. This section of highway is of particular interest, as the highway runs in parallel to the approach path of aircraft and crosses the approach path 3.7 km before the aircraft touches down (the flight altitude is only 200 m above the ground). For this experiment, we distributed six Septentrio Mosaic x5 GNSS receivers as sensors along the highway and monitored this section for five months. We analyzed the data with AGC monitoring, CN0 monitoring, and baseband sample monitoring to identify interference along the highway that could affect sensors along the descending flight trajectory. During the period of this experiment, we saw events that we believe could cause potential safety risks and problems for aviation safety. In our analysis, we focused on the statistical evaluation of the temporal repetitions, in particular the times of day that see more interference and the frequencies at which more interference occurs. Additionally, we analyzed the performance of different algorithms for dealing with large datasets. The results provide new insight into potential monitoring stations near airports and raise awareness of potential risks and vulnerabilities in aviation safety as well as automated driving along highways.

We propose an upwind finite volume method for a system of two kinetic equations in one dimension that are coupled through nonlocal interaction terms. These cross-interaction systems were recently obtained as the mean-field limit of a second order system of ordinary differential equations for two interacting species. Models of this kind are encountered in a myriad of contexts, for instance, to describe large systems of indistinguishable agents such as cell colonies, flocks of birds, schools of fish, herds of sheep. The finite volume method we propose is constructed to conserve mass and preserve positivity. Moreover, convex functionals of the discrete solution are controlled, which we use to show the convergence of the scheme. Finally, we investigate the scheme numerically.