Virtual element method for numerical simulation of Burgers’-Fisher equation on convex and non-convex meshes

A modified version of finite element method is considered for solving the combined non-linear time-dependent Burgers’ and Fisher equations. These equations are well-known in mathematical biology and have a wide range of applications. The virtual element method is one of the robust numerical methods. In this paper, a virtual process and a Euler-backward scheme are introduced for discretization in spatial and time direction, respectively. Our numerical scheme can achieve the optimal error rates based on the degree of our virtual space. The efficiency and flexibility of the proposed method is investigated by providing numerical outcomes on convex and non-convex polygonal meshes.