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Name: Edoardo BONETTI
Current position: PhD student in Scientific Computing and Modelling
Topic of master thesis: Numerical method for Weak Gravitational Formulation
Supervisor: Prof. Joachim SCHÖBERL

My research lies at the intersection of numerical analysis and mathematical physics, with a focus on the finite element method in general relativity. Like many mathematicians, I first encountered finite elements during my master’s studies, where the method is often presented as a mature and well-established framework. Students typically learn how functional analysis, approximation theory, and numerical implementation fit together to form a powerful tool for solving partial differential equations.

It was only when I began working on my master’s thesis and later my PhD under the guidance of Prof. Schöberl that I realized that this “finished product” is far from a ready-to-use tool in many cases. Finite element methods originally emerged from very practical problems in mechanics and were gradually extended to more complex systems, such as Maxwell’s equations, which require weaker function spaces and more refined mathematical structures. These extensions raise subtle analytical and numerical questions that continue to motivate research today; in particular, we study how to approximate solutions in terms of generalized functions.

In my work, I focus on finite element discretization for problems arising in general relativity, in particular on the simulation of (non)linear gravitational waves. What fascinates me most is the interplay between the continuous mathematical model, the discrete finite element space, and the resulting matrix–vector algebra. Each level has its own challenges, and progress usually requires moving back and forth between them. Many of the challenges I work on arise from understanding how properties of the continuous equations carry over to the discrete setting and how this affects the behavior of numerical methods in practice.

By the end of my PhD, I hope to have developed the background needed to engage with the more advanced branches of this subject.