# Parametric finite element approximations of curvature driven interface evolutions

## TL;DR

This paper presents efficient parametric finite element methods for simulating curvature-driven surface evolutions, ensuring stable computations with good mesh properties across various complex flows.

## Contribution

It introduces novel computational techniques based on a weak formulation for mean curvature, improving mesh stability and applicability to multiple curvature-driven phenomena.

## Key findings

- Methods demonstrate stability and mesh quality
- Applicable to diverse curvature flows
- Showcases effectiveness in biomembrane modeling

## Abstract

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 avoid mesh coalescence and very non-uniform meshes. Mean curvature flow, surface diffusion, anisotropic geometric flows, solidification, two-phase flow, Willmore and Helfrich flow as well as biomembranes are treated. We show stability results as well as results explaining the good mesh properties.

---
Source: https://tomesphere.com/paper/1903.09462