In this article we consider finite element methods for approximating the solution of partial
differential equations on surfaces. We focus on surface finite elements on triangulated …

We present a mathematical and a computational framework for the modelling of cell motility.
The cell membrane is represented by an evolving surface, with the movement of the cell …

Parametric finite elements lead to very efficient numerical methods for surface evolution
equations. We introduce several computational techniques for curvature driven evolution …

A high-order and energy stable scheme is developed to simulate phase-field models by
combining the semi-implicit spectral deferred correction (SDC) method and the energy …

In this paper, we will investigate the first-and second-order implicitexplicit schemes with
parameters for solving the Allen-Cahn equation. It is known that the Allen-Cahn equation …

We use the evolving surface finite element method to solve a Cahn–Hilliard equation on an
evolving surface with prescribed velocity. We start by deriving the equation using a …

In this paper, we design, analyze and numerically validate an unconditionally energy stable
second order numerical method for solving the Allen–Cahn equation which represents a …

In this article, we present a second-order in time implicit–explicit (IMEX) local discontinuous
Galerkin (LDG) method for computing the Cahn–Hilliard equation, which describes the …

Abstract The Allen–Cahn equation is a fundamental partial differential equation that
describes phase separation and interface motion in materials science, physics, and various …

We present numerical simulations for the surface Cahn–Hilliard equation which describes
phase separation phenomenon occurred on general surfaces. The spatial discretization is …