应用数学和力学2025，Vol.46Issue(12)：1612-1621,10.DOI:10.21656/1000-0887.450341
分数阶对流方程的全离散间断Galerkin方法
A Fully Discrete Discontinuous Galerkin Method for Fractional Convection Equations
摘要
Abstract
Fractional derivatives have received extensive attention due to their advantages in describing anoma-lous phenomena in nature.The numerical solutions to a class of convection equations containing temporal Capu-to-Hadamard fractional derivatives were studied.The L1 method was adopted to approximate the time deriva-tive,and the discontinuous Galerkin finite element method was used to approximate the spatial direction,thus to obtain the fully discrete numerical scheme for the equations.With the discrete Gronwall inequality,the stabil-ity,convergence and error estimates of the scheme were analyzed.Finally,numerical examples verify the cor-rectness of the proposed theoretical method.关键词
分数阶对流/间断Galerkin方法/全离散/稳定性/收敛性Key words
fractional convection/discontinuous Galerkin method/fully discrete/stability/convergence分类
数理科学引用本文复制引用
李晓婷,王震..分数阶对流方程的全离散间断Galerkin方法[J].应用数学和力学,2025,46(12):1612-1621,10.基金项目
国家自然科学基金(12101266) （12101266）
