一维反应扩散问题的时空谱元方法
A Space-Time Spectral Method for One-Dimensional Reaction-Diffusion Equation
摘要: 以一维反应扩散方程为模型，提出了一种时空谱元方法。在空间方向上应用局部间断Galerkin谱元法。在每个空间子区域上按Legendre-Galerkin方法生成格式，并且在边界处使用交替形式的数值流通量处理跳跃项。在时间方向上采用Legendre Dual-Petrov-Galerkin谱元法进行离散。给出了全离散格式的收敛性分析。线性及非线性问题的数值结果验证了该方法的有效性。
Abstract: Taking the one-dimensional reaction-diffusion equation as a model，a space-time spectral element method is proposed. We apply the local discontinuous Galerkin spectral element method in space direction. The scheme is formulated in the Legendre-Galerkin spectral form on each space subin-terval, while the inner boundary is dealt with alternating fluxes. The Legendre Dual-Petrov-Galerkin spectral element method is used to discretize the equation in time direction. The convergence analysis of the fully discrete scheme is given. The numerical results of some linear and nonlinear equations show the effectiveness of our method.
文章引用：朱欣怡, 吴华. 一维反应扩散问题的时空谱元方法[J]. 理论数学, 2021, 11(5): 752-766. https://doi.org/10.12677/PM.2021.115090

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