University of Kashan Mathematics Interdisciplinary Research 2538-3639 9 1 2024 03 01 Virtual‎ ‎Element‎ ‎Method‎ ‎for‎ Numerical Simulation of Burgers-Fisher Equation on Convex‎ ‎and Non-Convex Meshes 1 22 114194 10.22052/mir.2023.252806.1403 EN AllahBakhsh Yazdani Cherati ‎Department of Applied Mathematics‎, Faculty of Mathematical Sciences, ‎University of Mazandaran,‎ Babolsar‎, ‎I‎. ‎R‎. ‎Iran Hamid Momeni ‎Department of Applied Mathematics‎, Faculty of Mathematical Sciences, ‎University of Mazandaran,‎ Babolsar‎, ‎I‎. ‎R‎. ‎Iran Journal Article 2023 04 16 ‎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.<br />  https://mir.kashanu.ac.ir/article_114194_c9fcaef88e41c44d86e60082fb99a92c.pdf