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 …

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

We discuss an O-type multi-point flux approximation finite volume scheme for the
discretization of a system modelling two‐phase flow in porous media. The particular feature …

Equations of the interfacial convection and convection-diffusion describing the transport of
surfactants, and more general interfacial balance laws, in the context of a three-dimensional …

This thesis is concerned with motion planning for the classical two-phase Stefan problem in
level set formulation. The interface separating the fluid phases from the solid phases is …

We study a two phase porous media flow model where dynamic effects are included in the
capillary pressure. We present a finite volume method for the simulation of the solution. The …

We present a framework for handling cut cells in a high order discontinuous Galerkin (DG)
context. To describe the boundary between fluid phases, we use a level-set formulation …

In this paper we shall develop a face-based local tangential lifting method to handle the
problem of discrete conservation laws for diffusion equations and solve Cahn-Hilliard …

We present a finite volume scheme for anisotropic diffusion on evolving hypersurfaces. The
underlying motion is assumed to be described by a fixed, not necessarily normal, velocity …