文章基本信息

标题：Local Discontinuous Galerkin Methods Coupled with Implicit Integration Factor Methods for Solving Reaction-Cross-Diffusion Systems
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作者：Na An ; Xijun Yu ; Chaobao Huang 等
期刊名称：Discrete Dynamics in Nature and Society
印刷版ISSN：1026-0226
电子版ISSN：1607-887X
出版年度：2016
卷号：2016
DOI：10.1155/2016/5345032
出版社：Hindawi Publishing Corporation
摘要：We present a new numerical method for solving nonlinear reaction-diffusion systems with cross-diffusion which are often taken as mathematical models for many applications in the biological, physical, and chemical sciences. The two-dimensional system is discretized by the local discontinuous Galerkin (LDG) method on unstructured triangular meshes associated with the piecewise linear finite element spaces, which can derive not only numerical solutions but also approximations for fluxes at the same time comparing with most of study work up to now which has derived numerical solutions only. Considering the stability requirement for the explicit scheme with strict time step restriction (), the implicit integration factor (IIF) method is employed for the temporal discretization so that the time step can be relaxed as . Moreover, the method allows us to compute element by element and avoids solving a global system of nonlinear algebraic equations as the standard implicit schemes do, which can reduce the computational cost greatly. Numerical simulations about the system with exact solution and the Brusselator model, which is a theoretical model for a type of autocatalytic chemical reaction, are conducted to confirm the expected accuracy, efficiency, and advantages of the proposed schemes.