Weak Galerkin finite element method for an inhomogeneous Brusselator model with cross-diffusion

A  new  weak  Galerkin  finite  element  method  is  applied  for  time dependent  Brusselator  reaction-diffusion systems by using discrete weak  gradient operators over discontinuous weak functions. In this work, we consider the lowest order weak Galerkin finite element space $(P_{0},P_{0},RT_{0})$. Discrete weak gradients are defined in Raviart-Thomas space.  Thus we employ this approximate space on triangular mesh for solving unknown concentrations $ (u,v)$ in   Brusselator reaction-diffusion systems. Based on a weak varitional form, semi-discrete and fully-discrete weak Galerkin finite element scheme are obtained. In  addition, the paper  presents some  numerical  results to illustrate  the  power  of  proposed  method.