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 thecombined non-linear time-dependent burgers’ and fisher equations. these equationsare well-known in mathematical biology and have a wide range of applications. thevirtual element method is one of the robust numerical methods. in this paper, a virtualprocess and a euler-backward scheme are introduced for discretization in spatial andtime direction, respectively. our numerical scheme can achieve the optimal error ratesbased on the degree of our virtual space. the efficiency and flexibility of the proposedmethod is investigated by providing numerical outcomes on convex and non-convexpolygonal meshes.