This chapter surveys recent numerical advances in the phase field method for geometric
surface evolution and related geometric nonlinear partial differential equations (PDEs) …

Page 1 Lecture Notes in Mathematics Filippo Gazzola Hans-Christoph Grunau Guido Sweers
Polyharmonic Boundary Value Problems 1991 Positivity Preserving and Nonlinear Higher …

This review concerns the computation of curvature-dependent interface motion governed by
geometric partial differential equations. The canonical problem of mean curvature flow is that …

We consider the L2 gradient flow for the Willmore functional. In [5] it was proved that the
curvature concentrates if a singularity develops. Here we show that a suitable blowup …

The convergence property of the discrete Laplace–Beltrami operators is the foundation of
convergence analysis of the numerical simulation process of some geometric partial …

A new formulation for the Euler–Lagrange equation of the Willmore functional for immersed
surfaces in ℝ m is given as a nonlinear elliptic equation in divergence form, with non …

A level set formulation of Willmore flow is derived using the gradient flow perspective.
Starting from single embedded surfaces and the corresponding gradient flow, the metric is …

We propose a new algorithm for the computation of Willmore flow. This is the L 2-gradient
flow for the Willmore functional, which is the classical bending energy of a surface. Willmore …

This work considers the question of whether mean‐curvature flow can be modified to avoid
the formation of singularities. We analyze the finite‐elements discretization and demonstrate …

We use various nonlinear partial differential equations to efficiently solve several surface
modelling problems, including surface blending, N-sided hole filling and free-form surface …