70 citations · 93 across the 11 of their papers we have counts for
8 papers · 1 filter
Evolving finite elements for advection diffusion with an evolving interface
C. M. Elliott, T. Ranner, P. Stepanov
The aim of this paper is to develop a numerical scheme to approximate evolving interface problems for parabolic equations based on the abstract evolving finite element framework pr…
A stable finite element method for low inertia undulatory locomotion in three dimensions
Thomas Ranner
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 - represen…
A unified theory for continuous in time evolving finite element space approximations to partial differential equations in evolving domains
Charles M. Elliott, Thomas Ranner
We develop a unified theory for continuous in time finite element discretisations of partial differential equations posed in evolving domains including the consideration of equatio…
Evolving surface finite element methods for random advection-diffusion equations
Ana Djurdjevac, Charles M. Elliott, Ralf Kornhuber +1
In this paper, we introduce and analyse a surface finite element discretization of advection-diffusion equations with uncertain coefficients on evolving hypersurfaces. After statin…
Solving reaction-diffusion equations on evolving surfaces defined by biological image data
Till Bretschneider, Cheng-Jin Du, Charles M. Elliott +2
We present a computational approach for solving reaction-diffusion equations on evolving surfaces which have been obtained from cell image data. It is based on finite element space…
An unfitted discontinuous Galerkin scheme for conservation laws on evolving surfaces
Christian Engwer, Thomas Ranner, Sebastian Westerheide
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…
Unfitted finite element methods using bulk meshes for surface partial differential equations
Klaus Deckelnick, Charles M. Elliott, Thomas Ranner
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 ke…
Evolving surface finite element method for the Cahn-Hilliard equation
Charles M. Elliott, Thomas Ranner
We use the evolving surface finite element method to solve a Cahn- Hilliard equation on an evolving surface with prescribed velocity. We start by deriving the equation using a cons…