Implicit-explicit timestepping with finite element approximation of reaction-diffusion systems on evolving domains (Q2855109)

The paper presents an implicit-explicit time stepping finite element scheme for the transient reaction-diffusion systems (RDS) over an evolving domain. The initial-boundary value problem consists of the convective diffusion equation subjected to Neumann boundary conditions. The convection is induced by the material deformation due to the evolution of the domain. A weak formulation of the continuous RDS is developed. A semi-discrete and fully discrete finite element schemes are constructed and their error bounds are determined. Several lemmas and theorems are derived to establish the convergence and the stability of the schemes. The order of convergence is tested for a spatially linear and nonlinear periodic evolution. An example of Schnakenberg kinetics over a linear periodic evolving domain is considered to demonstrate the utility of the scheme.