Codes for all publications are available via GitLab, or upon request.

## Mean curvature flow

Numerical experiments for mean curvature flow algorithm from our paper.

A dumbbell-shaped surface developing a pinch singularity along the flow. Comparing Dziuk's algorithm to ours (without and with normalisation of the normal vector, and a zoom-in on the singularity):

An Angenent torus remaining self-similar as it numerically evolves under the mean curvature flow:

## Forced mean curvature flow

Numerical experiments for a tumour growth model using the algorithm from the paper (with two different reaction parameters \(\gamma=30\) and \(300\), left and right):

## Willmore flow

Some numerical experiments for Willmore flow using the algorithm analysed in the paper.

Topologically spherical objects are known to converge to a sphere, while minimising the Willmore energy \( ( W(\Gamma) \to 8\pi ) \):

Surfaces of genus 1 are converging to a Clifford torus minimising the Willmore energy \( ( W(\Gamma) \to 4\pi^2 ) \) (top and side view):

## Generalised mean curvature flows

Numerical experiments for an algorithm for generalised mean curvature flows, i.e. the surface velocity is given by \(v = - V(H) \nu_\Gamma\).

A non-convex dumbbell-shaped surface evolving towards a singularity along *inverse mean curvature flow* (\(V(H) = - 1 / H\)):

The same surface evolving towards a pinch singularity along *powers of mean curvature flow* (\(V(H) = H^2\)):

A genus-5 surface evolving under *powers of inverse mean curvature flow* (\(V(H) = - 1 / H^2 \)):

## Mean curvature flow in higher codimension

Numerical experiments for an algorithm for mean curvature flow in *codimension two*.

A trefoil knot evolving under *mean curvature flow in codimension 2* (with and without rescaling):

## Mean curvature flow interacting with diffusion

Numerical experiments for an algorithm for the *interaction of mean curvature flow and diffusion* on closed surfaces.
This model was first developed and studied by Bürger (UR).

Mean curvature flow interacting with diffusion on an elongated ellipsoid, and a comparison with pure mean curvature flow.

Numerical solutions for the mean curvature flow interacting with diffusion illustrating slow diffusion through a thin neck (left), and the possibility for self-intersecting solutions (right).

## Numerical surgery for mean curvature flow

Inspired by surgery process of Huisken & Sinestrari and Brendle & Huisken, this paper proposes a numerical mean curvature flow algorithm with surgery for surfaces.

Resolving a pinch singularity of a dumbbell-shaped surface, and a more complicated example for a torus and a sphere joined by a thin neck.