Local Discontinuous Galerkin Methods for Reaction-Diffusion Systems on Unstructured Triangular Meshes

摘要

In this paper, on two-dimension unstructured meshes, a fully-discrete scheme is presented for the reaction-diffusion systems, which are often used as mathematical models for many biological, physical and chemical applications. By using local discontinuous Galerkin (LDG) method, the scheme can derive the numerical approximations not only for solutions but also for their gradients at the same time. In addition, the scheme employs the implicit integration factor (IIF) method for temporal discretization, which allows us to take the time-step as δt = O(h_(min)), and can be computed element by element, so that it reduces the computational cost greatly. Numerical simulations for the chlorite-iodide-malonic acid (CIMA) model demonstrate the expected behavior of the solutions, the efficiency and advantages of the proposed scheme.