A Fully Discrete Discontinuous Galerkin Method for Fractional Convection Equations

LI Xiaoting; WANG Zhen

doi:10.21656/1000-0887.450341

Volume 46 Issue 12

Dec. 2025

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LI Xiaoting, WANG Zhen. A Fully Discrete Discontinuous Galerkin Method for Fractional Convection Equations[J]. Applied Mathematics and Mechanics, 2025, 46(12): 1612-1621. doi: 10.21656/1000-0887.450341

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A Fully Discrete Discontinuous Galerkin Method for Fractional Convection Equations

doi: 10.21656/1000-0887.450341

LI Xiaoting¹,
WANG Zhen^{2
,
,}

1. Jingjiang College, Jiangsu University, Zhenjiang, Jiangsu 212013, P.R.China;
2. School of Mathematical Sciences, Jiangsu University, Zhenjiang, Jiangsu 212013, P.R.China

Funds:

The National Science Foundation of China(12101266)

Received Date: 2024-12-30
Rev Recd Date: 2025-02-17

Available Online: 2025-12-31

Abstract

Abstract

Fractional derivatives have received extensive attention due to their advantages in describing anomalous phenomena in nature. The numerical solutions to a class of convection equations containing temporal Caputo-Hadamard fractional derivatives were studied. The L1 method was adopted to approximate the time derivative, 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 stability, convergence and error estimates of the scheme were analyzed. Finally, numerical examples verify the correctness of the proposed theoretical method.
- fractional convection,
- discontinuous Galerkin method,
- fully discrete,
- stability,
- convergence

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References(18)

References

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