| 分数阶对流扩散方程的特征有限元方法 |
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| 引用本文： | 朱晓钢,聂玉峰,王俊刚,袁占斌.分数阶对流扩散方程的特征有限元方法[J].计算物理,2017,34(4):417-424. |
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| 作者姓名： | 朱晓钢 聂玉峰 王俊刚 袁占斌 |
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| 作者单位： | 西北工业大学应用数学系, 陕西 西安 710129 |
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| 基金项目： | 国家自然科学基金（11471262，11501450）资助项目 |
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| 摘 要： | 讨论非线性分数阶对流扩散方程的特征有限元方法.利用特征线法和分数阶有限元框架，构建一种基于特征方向的全离散有限元格式.模拟物理问题，并在数值上与常规有限元格式进行比较，计算结果表明：该方法能准确地捕捉到控制方程的精确解，即使是在对流效应占优时，也具有稳定性好和逼近精度高等特征.
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| 关 键 词： | 分数阶微积分 对流扩散方程 特征有限元方法 |
| 收稿时间： | 2016-06-23 |
| 修稿时间： | 2016-09-12 |
A Characteristic Finite Element Method for Fractional Convection-Diffusion Equations |
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| ZHU Xiaogang,NIE Yufeng,WANG Jungang,YUAN Zhanbin.A Characteristic Finite Element Method for Fractional Convection-Diffusion Equations[J].Chinese Journal of Computational Physics,2017,34(4):417-424. |
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| Authors: | ZHU Xiaogang NIE Yufeng WANG Jungang YUAN Zhanbin |
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| Institution: | Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710129, China |
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| Abstract: | A characteristic finite element method (FEM) is proposed for nonlinear fractional convection-diffusion equations. With the characteristic technique and fractional FEM framework, a fully discrete characteristic finite element scheme is constructed. It is utilized to simulate physical systems and studied in contrast with conventional schemes. It is demonstrated that the method captures exact solutions of governing equations well. The method enjoys good stability and high accuracy even if convection dominates diffusion essentially. |
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| Keywords: | fractional calculus convection-diffusion equation characteristic FEM |
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