At its board meeting on 29 September 2025, the Austrian Science Fund (FWF) approved the stand-alone project “Adaptive Uzawa-FEM for Nonlinear PDEs”(project number PAT3446525, opens an external URL in a new window) led by Prof. Dirk PRAETORIUS. Within this project, algorithms for the numerical solution of nonlinear partial differential equations (PDEs) will be investigated. The goal is to develop algorithms that optimally balance discretization, linearization, and solver errors so that the overall error decreases optimally with respect to computational time. A particular focus lies on coupled PDE systems, where, in analogy to the classical Uzawa algorithm for the Stokes system, the linearization will be performed at the level of the continuous PDE to exploit any PDE-inherent structure.

In the same meeting, the FWF also approved a change in project leadership for the stand-alone project “Optimal Robust Solvers for Reliable and Efficient AFEMs”(project number PAT3699424, opens an external URL in a new window). Prof. Dirk Praetorius will take over as principal investigator from Dr Ani MIRACI, who joined Sorbonne University Paris in September 2025. Following this positive decision by the FWF, Dirk Praetorius (previously co-PI and collaboration partner of the project) and Ani Miraci have swapped roles, allowing them to continue their joint research in this field.

In total, the workgroup“Numerical Analysis of PDEs” led by Prof. Dirk Praetorius will receive nearly EUR 1 million over the next four years to further advance its research on cost-optimal adaptive methods for solving partial differential equations.
The ASC extends its sincere congratulations on this outstanding achievement!