About me
I am a postdoctoral researcher at the Technical University of Berlin in the research group Differential Equations, headed by Prof. Dr. Etienne Emmrich.
From March through September 2026, I am a Distinguished Fellow at George Mason University (Fairfax, VA, USA), hosted by Prof. Dr. Harbir Antil.
Previously, I held a postdoctoral position at the University of Freiburg, where I also completed my PhD under the supervision of Prof. Dr. Michael Růžička. From July 2023 to April 2024, I was a Walter Benjamin Fellow of the German Research Foundation (DFG), conducting research on numerical methods for so-called smart fluids in collaboration with Prof. Dr. Luigi C. Berselli at the University of Pisa.
Research profile
I develop mathematically rigorous and computationally reliable methods for nonlinear PDEs, nonsmooth variational problems, and complex fluid flows. My research has two main pillars—duality-based numerical methods and the analysis and numerics of non-Newtonian and smart fluids—complemented by data-informed methods for parametric PDEs and generative modelling.
Duality-based numerical methods: Convex duality and primal-dual error identities for a posteriori and a priori error analysis, adaptive mesh refinement, and error control for iterative solvers; robust solvers based on semi-implicit gradient flows and proximal semismooth Newton methods; and extensions to subgradient flows, higher-order discretisations, PDE-constrained optimisation, and learning-enhanced iterative solvers. Applications include obstacle and Signorini problems, elastoplastic torsion, ROF/TV imaging, $p$-Dirichlet and $p$-Stokes systems, optimal insulation, and digital twins for structural health monitoring.
Analysis and numerics of non-Newtonian and smart fluids: Existence theory based on generalised pseudomonotonicity and hydromechanical compensated compactness; finite element and discontinuous Galerkin convergence analysis via discrete counterparts of these principles; and a priori error analysis supported by application-oriented numerical experiments. Models include generalised Newtonian $p$-flows, micropolar and variable-exponent electro-rheological fluids, space-time-dependent $p(t,x)$-Navier–Stokes systems, pulsatile pipe flows, and pressure approximation under slip conditions.
Deep-Ritz-type PINNs for high-dimensional parametric PDEs: Neural approximation of parameter-to-solution maps, with a current focus on parametric $p(\mu)$-Stokes systems.
Quantum-hydrodynamic generative modelling: Deterministic PDE-based generative methods using the Madelung representation, Schrödinger dynamics, and PDE-constrained terminal matching.