We discuss recent advances on robust unfitted finite element methods on cut meshes. These
methods are designed to facilitate computations on complex geometries obtained, for …

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 …

Several cellular activities, such as directed cell migration, are coordinated by an intricate
network of biochemical reactions which lead to a polarised state of the cell, in which cellular …

The Cahn–Hilliard equation is one of the most common models to describe phase
separation processes of a mixture of two materials. For a better description of short-range …

The paper introduces a new finite element numerical method for the solution of partial
differential equations on evolving domains. The approach uses a completely Eulerian …

In this article, we formulate new models for coupled systems of bulk-surface reaction–
diffusion equations on stationary volumes. The bulk reaction–diffusion equations are …

Signalling molecules play an important role for many cellular functions. We investigate here
a general system of two membrane reaction–diffusion equations coupled to a diffusion …

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 devise a moving mesh finite element method for the approximate solution
of coupled bulk–surface reaction–diffusion equations on an evolving two dimensional …

We develop a cut finite element method for a second order elliptic coupled bulk-surface
model problem. We prove a priori estimates for the energy and L^ 2 L 2 norms of the error …