Efficient computation of curvature driven interface evolution

Parametric finite elements lead to very efficient numerical methods for surface evolution equations. We introduce several computational techniques for curvature driven evolution equations based on a weak formulation for the mean curvature. The approaches discussed, in contrast to many other methods, have good mesh properties that prevent mesh coalescence and very nonuniform meshes. Mean curvature flow, surface diffusion, anisotropic geometric flows, Willmore flow as well as free boundary problems are treated. We show stability results as well as results explaining the good mesh properties. Finally, we address new developments for numerically solving Navier-Stokes equations on evolving surfaces.

This initiative is part of the “Ph.D. Lectures” activity of the project "Departments of Excellence 2023-2027" of the Department of Mathematics of Politecnico di Milano. This activity consists of seminars open to Ph.D. students, followed by meetings with the speaker to discuss and go into detail on the topics presented at the talk.

Contatti:
paola.antonietti@polimi.it
maurizio.grasselli@polimi.it
andrea.signori@polimi.it