In this paper, we define new unfitted finite element methods for numerically approximating the solution of surface partial differential equations using bulk finite elements. The key idea is that theâ€¦ (More)

We consider a coupled bulk-surface system of partial differential equations with nonlinear coupling modeling receptor-ligand dynamics. The model arises as a simplification of a mathematical model forâ€¦ (More)

We explore an optimal partition problem on surfaces using a computational approach. The problem is to minimise the sum of the first Dirichlet Laplaceâ€“Beltrami operator eigenvalues over a given numberâ€¦ (More)

Philosophical transactions of the Royal Societyâ€¦

2018

Animal neuromechanics describes the coordinated self-propelled movement of a body, subject to the combined effects of internal neural control and mechanical forces. Here we use a computational modelâ€¦ (More)

Motivated by considering partial differential equations arising from conservation laws posed on evolving surfaces, a new numerical method for an advection problem is developed and simple numericalâ€¦ (More)

In this paper, we introduce and analyse a surface finite element discretization of advection-diffusion equations with uncertain coefficients on evolving hypersurfaces. After stating uniqueâ€¦ (More)