virtual‎ ‎element‎ ‎method‎ ‎for‎ numerical simulation of burgers-fisher equation on convex‎ ‎and non-convex meshes

‎we present an enhanced approach to solving the combined non-linear time-dependent burgers-fisher equation‎, ‎which is widely used in mathematical biology and has a broad range of applications‎. ‎our proposed method employs a modified version of the finite element method‎, ‎specifically the virtual element method‎, ‎which is a robust numerical approach‎. ‎we introduce a virtual process and an euler-backward scheme for discretization in the spatial and time directions‎, ‎respectively‎. ‎our numerical scheme achieves optimal error rates based on the degree of our virtual space‎, ‎ensuring high accuracy‎. ‎we evaluate the efficiency and flexibility of our approach by providing numerical results on both convex and non-convex polygonal meshes‎. ‎our findings indicate that the proposed method is a promising tool for solving non-linear time-dependent equations in mathematical biology‎.