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

Document Type : Research Article

Authors

1 Department of Applied Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran

2 Department of Applied Mathematics Faculty of Mathematical Sciences Tarbiat Modares University,Tehran,Iran

Abstract

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.

Keywords

Journal of Mathematical Modeling
Volume 7, Issue 3
September 2019
Pages 277-285

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