二维非线性反应扩散方程的局部间断Galerkin谱元法  

LOCAL DISCONTINUOUS GALERKIN SPECTRAL ELEMENT METHOD FOR NONLINEAR REACTION-DIFFUSION EQUATIONS

作　　者：汪海鹭 吴华[1] Wang Hailu;Wu Hua(College of Sciences,Shanghai University,Shanghai 200444,China)

机构地区：[1]上海大学理学院,上海200444

出　　处：《数值计算与计算机应用》2020年第1期1-18,共18页Journal on Numerical Methods and Computer Applications

基　　金：国家自然科学基金(11571225).

摘　　要：本文提出了二维非线性反应扩散方程的局部间断Galerkin谱元法.在空间方向上采用了Legendre-Galerkin Chebyshev谱配置法,即在每个子区域上,该格式按Legendre-Galerkin谱方法形成,子区域交界面处的跳跃项利用数值流量进行处理,非线性项采用在Chebyshev-Gauss-Lobatto点上的插值进行计算.时间方向上采用四阶低存储Runge-Kutta方法.文中给出了半离散格式下的稳定性和收敛性分析,以及单区域和多区域算法的数值算例,并与间断Galerkin有限元方法进行比较.In this paper,local discontinuous Galerkin spectral element method for nonlinear reactiondiffusion equations are considered.The Legendre-Galerkin Chebyshev collocation spectral method is used in the spatial direction,which means the schemes are formulated with the Legendre-Galerkin method in each subdomain and the jump terms are controlled by numerical flux at cell boundaries.The nonlinear term is interpolated through the ChebyshevGauss-Lobatto points.Meanwhile,the fourth-order low-storage Runge-Kutta schemes are used in time discretization.Stability and the rate of convergence of the method are proved.We also give some numerical examples which coincide with the theoretical analysis.And the numerical results are compared with those obtained by discontinuous Galerkin finite element method.

关 键 词：局部间断Galerkin方法 谱元法 Legendre-Galerkin Chebyshev配置法 反应扩散方程 

分 类 号：O241.82[理学—计算数学]