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A unified theory for continuous in time evolving finite element space approximations to partial differential equations in evolving domains

We develop a unified theory for continuous in time finite element discretisations of partial differential equations posed in evolving domains including the consideration of equations posed on evolving surfaces and bulk domains as well coupled …

A stable finite element method for low inertia undulatory locomotion in three dimensions

We present and analyse a numerical method for understanding the low-inertia dynamics of an open, inextensible viscoelastic rod - a long and thin three dimensional object - representing the body of a long, thin microswimmer. Our model allows for both …

Evolving surface finite element methods for random advection-diffusion equations

Even though random partial differential equations (PDEs) have become a very active field of research, the analysis and numerical analysis of random PDEs on surfaces still appears to be in its infancy. In this paper, we introduce and analyse a …

Signatures of proprioceptive control in C. elegans locomotion

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 model to identify effects of neural and mechanical …

Coupled bulk-surface free boundary problems arising from a mathematical model of receptor-ligand dynamics

We consider a coupled bulk-surface system of partial differential equations with nonlinear coupling modelling receptor-ligand dynamics. The model arises as a simplification of a mathematical model for the reaction between cell surface resident …

A computational approach to an optimal partition problem on surfaces

Evolving surface finite element method for the Cahn-Hilliard equation

Unfitted finite element method using bulk meshes for surface partial differential equations

Finite element analysis for a coupled bulk-surface partial differential equation

In this paper, we define a new finite element method for numerically approximating the solution of a partial differential equation in a bulk region coupled with a surface partial differential equation posed on the boundary of the bulk domain. The key …