Project
Research on PDEs on curved surfaces mostly focuses on scalar equations with weak coupling between surface geometry and the PDE. Existing numerical approaches for flat spaces can be adapted with minor modifications. However, for vector- and tensor-valued surface PDEs, these methods fall short. A research unit is bringing together experts from various fields to tackle this challenge. They aim to understand mathematical complexities by studying specific problems in biophysics, mechanics, and other areas. These problems involve nonlinear vector- and tensor-valued surface PDEs that arise due to surface geometry. Reliable simulations in these active research fields are expected to drive further progress.