Finite Element Method Applied to Gray-Scott Reaction-Diffusion Problem. Using FEniCs Software

Abstract

The Gray-Scott problem is among the reaction –diffusion systems showing patterns that stand out by showing self-replicating patterns (spots). This pattern formulation is a suitable interplay between diffusion and reaction.  Here we show in details the spot multiplication process of the Gray-Scott reaction-diffusion problem using finite element method, where the finite element mesh is generated using an external and a free three dimensional finite element mesh generator called Gmsh.  And Numerical experiment is performed using a free software package called FEniCs.

Keywords: Finite Element Methods, Gray-Scott, self-replication,  FEniCs, Gmsh