水沙输运模型的间断有限元方法

张任鹏, 王 波, 王 强

doi:10.13371/j.cnki.chin.q.j.m.2024.04.002

数学季刊 >

2024 , Vol. 39 >Issue 4: 355 - 365

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2024.04.002

水沙输运模型的间断有限元方法

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1. School of Mathematics and Statistics, Henan University, Kaifeng 475004, China; 2. Henan Key Laboratory of Earth System Observation and Modeling, Henan University, Kaifeng 475004, China; 3. The Academy for Advanced Interdisplinary Studies, Henan University, Zhengzhou 450046, China; 4. Institute of Mathematics and Physics, Beijing Union University, Beijing 100101, China; 5. Institute of Fundamental and Interdisciplinary Sciences, Beijing Union University, Beijing 100101, China

ZHANG Ren-peng (1999-), male, native of Taian, Shandong, graduate student of Henan University, engages in PDE; WANG Bo (1976-), female, native of Liaocheng, Shandong, professor of Henan University, engages in PDE; WANG Qiang (1977-), male, native of Beijing, lecturer of Beijing Union University, engages in PDE.

收稿日期: 2024-03-08

网络出版日期: 2024-12-30

基金资助

Supported by the National Natural Science Foundation of China (Grant No. 41930643) and the Natural Science Foundation of Henan Province (Grant No. 232300420109).

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Discontinuous Galerkin Method for Hydrodynamic and Sediment Transport Model

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1. School of Mathematics and Statistics, Henan University, Kaifeng 475004, China; 2. Henan Key Laboratory of Earth System Observation and Modeling, Henan University, Kaifeng 475004, China; 3. The Academy for Advanced Interdisplinary Studies, Henan University, Zhengzhou 450046, China; 4. Institute of Mathematics and Physics, Beijing Union University, Beijing 100101, China; 5. Institute of Fundamental and Interdisciplinary Sciences, Beijing Union University, Beijing 100101, China

Received date: 2024-03-08

Online published: 2024-12-30

Supported by

Supported by the National Natural Science Foundation of China (Grant No. 41930643) and the Natural Science Foundation of Henan Province (Grant No. 232300420109).

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摘要

In this article, we propose and research a first-order, linearized discontinuous Galerkin method for the approximation of the hydrodynamic and sediment transport model. The method is decoupled and fully discrete, and is shown to be unconditionally
stable. Furthermore, error estimates are proved. Finally, the theoretical analysis is confirmed by numerical examples.

关键词： Discontinuous Galerkin method; Stability analysis; Error estimates

本文引用格式

张任鹏, 王波, 王强 . 水沙输运模型的间断有限元方法[J]. 数学季刊, 2024 , 39(4) : 355 -365 . DOI: 10.13371/j.cnki.chin.q.j.m.2024.04.002

Abstract

Key words： Discontinuous Galerkin method; Stability analysis; Error estimates

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