70 citations · 191 across the 17 of their papers we have counts for
9 papers · 1 filter
Finite element approximation of the enthalpy formulation for Stefan problems on evolving surfaces
Philip J. Herbert, Thomas Sales, Chandrasekhar Venkataraman
We propose, and analyse, a spatially discrete evolving surface finite element method for the approximation of the enthalpy formulation of the two-phase Stefan problem posed on an e…
Parallel two-scale finite element implementation of a system with varying microstructures
Omar Richardson, Omar Lakkis, Adrian Muntean +1
We propose a two-scale finite element method designed for heterogeneous microstructures. Our approach exploits domain diffeomorphisms between the microscopic structures to gain com…
Lumped finite element method for reaction-diffusion systems on compact surfaces
Massimo Frittelli, Anotida Madzvamuse, Ivonne Sgura +1
We propose and analyse a novel surface finite element method that preserves the invariant regions of systems of semilinear parabolic equations on closed compact surfaces in $\mathb…
A computational approach for mode isolation for reaction-diffusion systems on arbitrary geometries
Laura Murphy, Chandrasekhar Venkataraman, Anotida Madzvamuse
In this article we present a computational framework for isolating spatial patterns arising in the steady states of reaction-diffusion systems. Such systems have been used to model…
Whole cell tracking through the optimal control of geometric evolution laws
Konstantinos N. Blazakis, Anotida Madzvamuse, Constantino-Carlos Reyes-Aldasoro +2
Cell tracking algorithms which automate and systematise the analysis of time lapse image data sets of cells are an indispensable tool in the modelling and understanding of cellular…
Error analysis for an ALE evolving surface finite element method
Charles M. Elliott, Chandrasekhar Venkataraman
We consider an arbitrary-Lagrangian-Eulerian evolving surface finite element method for the numerical approximation of advection and diffusion of a conserved scalar quantity on a m…
Parameter identification problems in the modelling of cell motility
Wayne Croft, Charles M Elliott, Graham Ladds +3
We present a novel parameter identification algorithm for the estimation of parameters in models of cell motility using imaging data of migrating cells. Two alternative formulation…
Adaptive finite elements for semilinear reaction-diffusion systems on growing domains
Chandrasekhar Venkataraman, Omar Lakkis, Anotida Madzvamuse
We propose an adaptive finite element method to approximate the solutions to reaction-diffusion systems on time-dependent domains and surfaces. We derive a computable error estimat…
Implicit-explicit timestepping with finite element approximation of reaction-diffusion systems on evolving domains
Omar Lakkis, Anotida Madzvamuse, Chandrasekhar Venkataraman
We present and analyse an implicit-explicit timestepping procedure with finite element spatial approximation for a semilinear reaction-diffusion systems on evolving domains arising…