Abstract
We present and analyze an implicit--explicit timestepping procedure with finite el- ement spatial approximation for semilinear reaction--diffusion systems on evolving domains arising from biological models, such as Schnakenberg's (1979). We employ a Lagrangian formulation of the model equations which permits the error analysis for parabolic equations on a fixed domain but intro- duces technical difficulties, foremost the space-time dependent conductivity and diffusion. We prove optimal-order error estimates in the L∞(0,T;L2(Ω)) and L2(0,T;H1(Ω)) norms, and a pointwise stability result. We remark that these apply to Eulerian solutions. Details on the implementation of the Lagrangian and the Eulerian scheme are provided. We also report on a numerical experiment for an application to pattern formation on an evolving domain.