I am a postdoctoral researcher at the Technical University of Berlin in the group Differential Equations headed by Prof. Dr. Etienne Emmrich. Previously I held a Postdoc position the Department of Applied Mathematics at the University of Freiburg, where I also did my PhD under the supervision of Prof. Dr. Michael Růžička. From July 2023 to April 2024 I have been Fellow of the Walter-Benjamin-Program. My research project, which I conducted in collaboration with Prof. Dr. Luigi C. Berselli at the University of Pisa, aimed at theoretical and experimental investigation on numerical methods for so-called smart fluids.

Research interests

1. Error analysis for non-smooth, convex minimization problems on the basis of convex duality
   • A priori error analysis on the basis of discrete convex duality (especially a priori error identities);
   • A posteriori error analysis on the basis of continuous convex duality (especially a posteriori error identities);
   • Medius error analysis (i.e., best-approximation results);
   • Reconstruction formulas for (discrete) dual solutions from (discrete) primal solutions (and vice versa); (so-called generalized Marini formulas);
   • Adaptive mesh refinement by means of resulting local refinement indicators;
   • Iterative methods for non-smooth, convex minimizatioin problems (e.g., semi-discretized gradient flows, semi-smooth Newton methods, primal-dual iterations);
   • Model problems: $p$-Dirichlet problem, $p(x)$-Dirichlet problem, obstacle problem, Signorini problem, Rudin–Osher–Fatemi problem, elastisch-plastic torsions problem.
2. Numerical methods for smart fluids
   • Convergence analysis for finite element approximations for steady and unsteady problems;
   • A priori error analysis for finite element approximations for steady and unsteady problems;
   • Existence and regularity theory for steady and unsteady problems;
   • Application-oriented simulations (with applications from the field of engineering).
3. Convergence analysis for fully-discretizations of non-linear evolution equations
   • Convergence results for fully-discretizations without parabolic compactness theorems like Lions-Aubin or Simon, but on the basis of non-conforming (Bochner) pseudomonotonicity;
   • Hirano-Landes approach, i.e., convergence results for fully-discretizations on the basis of stationary compactness theorems (e.g., Rellich or non-conforming generalizations).
4. Discontinuous Galerkin (DG) type approximations for non-Newtonian fluids
   • Convergence analysis for steady and unsteady problems;
   • A priori error analysis for steady and unsteady problems;
   • Local Discontinuous Galerkin (LDG) approximations;
   • Symmetric Interior Penalty (SIP) approximations;
   • Quasi-optimality, i.e., best approximation results for irregular right-hand sides and without oscillation terms;