对流扩散方程的隐式全离散局部间断Galerkin方法

赵思敏; 宋灵宇

doi:10.13568/j.cnki.651094.651316.2024.04.09.0001

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对流扩散方程的隐式全离散局部间断Galerkin方法

更新时间：2026-01-21

- 对流扩散方程的隐式全离散局部间断Galerkin方法
- Journal of Xinjiang University (Natural Science Edition in Chinese and English) Vol. 41, Issue 5, Pages: 532-541(2024)
- 作者机构：
  
  长安大学理学院
- 作者简介：
- 基金信息：
- DOI：10.13568/j.cnki.651094.651316.2024.04.09.0001
  CLC： O241.82
- Published：2024
- 稿件说明：
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[1]赵思敏,宋灵宇.对流扩散方程的隐式全离散局部间断Galerkin方法[J].新疆大学学报(自然科学版中英文),2024,41(05):532-541.
[1]赵思敏,宋灵宇.对流扩散方程的隐式全离散局部间断Galerkin方法[J].新疆大学学报(自然科学版中英文),2024,41(05):532-541. DOI： 10.13568/j.cnki.651094.651316.2024.04.09.0001.

DOI：10.13568/j.cnki.651094.651316.2024.04.09.0001.

摘要

研究了对流扩散方程的隐式全离散局部间断Galerkin方法的稳定性和误差分析.将三阶隐式Runge-Kutta时间离散和具有广义交替数值流通量的LDG方法相结合得到全离散LDG格式

通过广义交替数值流通量

建立数值解和辅助解内积之间的关系

证明了全离散LDG格式的无条件稳定

同时引入广义Gauss-Radau投影

通过投影的逼近性质和一些基本不等式建立了数值方法的最优误差估计

最后通过数值实验验证该方法理论分析的正确性.

Abstract

The stability and error analysis of the implicit fully discrete local discontinuous Galerkin method for convection diffusion equations are studied. The fully discrete LDG format is obtained by combining the thirdorder level implicit Runge-Kutta time discretization and the LDG method with generalized alternating numerical flux. Based on the generalized alternating numerical flux

the relationship between the inner product of the numerical solution and the auxiliary solution is established

and the unconditional stability of the fully discrete local discontinuous Galerkin format is demonstrated. At the same time

the generalized Gauss-Radau projection is introduced

and the optimal error estimate is established by the approximation properties of the projection and some basic inequalities

and finally the correctness of the theoretical analysis of the method is verified by numerical experiments.

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references

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