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 …

A method is presented to solve two-phase problems involving soluble surfactants. The
incompressible Navier–Stokes equations are solved along with equations for the bulk and …

A method is presented to solve two-phase problems involving a material quantity on an
interface. The interface can be advected, stretched, and change topology, and material can …

A two-phase Newtonian surface fluid is modelled as a surface Cahn–Hilliard–Navier–Stokes
equation using a stream function formulation. This allows one to circumvent the subtleties in …

We present an abstract framework for treating the theory of well-posedness of solutions to
abstract parabolic partial di¤ erential equations on evolving Hilbert spaces. This theory is …

In this paper we consider the evolving surface finite element meth-od for the advection and
diffusion of a conserved scalar quantity on a moving surface. In an earlier paper using a …

We propose a numerical method for computing transport and diffusion on a moving surface.
The approach is based on a diffuse interface model in which a bulk diffusion–advection …

This paper presents a general theory and isogeometric finite element implementation for
studying mass conserving phase transitions on deforming surfaces. The mathematical …

We develop numerical methods for solving partial differential equations (PDE) defined on an
evolving interface represented by the grid based particle method (GBPM) recently proposed …

Numerical methods for approximating the solution of partial differential equations on
evolving hypersurfaces using surface finite elements on evolving triangulated surfaces are …