Abstract In this paper, an efficient method seeking the numerical solution of a time-fractional convection equation whose solution is not smooth at the starting time is presented. The Caputo time-fractional derivative of order in ( 0 , 1 ) is discretized by the L1 finite difference method using non-uniform meshes; and, for the spatial derivative the discontinuous Galerkin (DG) finite element method is used. The stability and convergence of the method are analyzed for two-dimensional domains, using Cartesian and a particular class of unstructured grids. At last, several numerical examples are carried out which support the theoretical analysis.

中文翻译：

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具有弱正则解的时间分数对流方程的非均匀 L1/不连续 Galerkin 近似

摘要 本文提出了一种求解起始时间不光滑的时间分数阶对流方程数值解的有效方法。( 0 , 1 ) 阶的 Caputo 时间分数阶导数通过 L1 有限差分方法使用非均匀网格离散化；并且，对于空间导数，使用不连续伽辽金 (DG) 有限元方法。使用笛卡尔和特定类别的非结构化网格对二维域分析该方法的稳定性和收敛性。最后给出了几个数值算例，为理论分析提供了支持。